## WORD PROBLEMS INVOLVING SIMILAR TRIAGNLES

Example 1 :

A ramp is built enable wheel-chair access to a building that is 24 cm above ground level. The ramp has a constant slope of 2 in 15, which means that for every 15 cm horizontally its rises 2 cm. Calculate the length of the base of the ramp.

In ∆DEC and ∆ABC,

<DCE = <ACB (A)

<DEC = <ABC (A)

Using AA theorem, the above triangles

∆DEC ~ ∆ABC

DE/AB = CD/CA = CE/BC

DE/AB = CE/BC

Let BE = x, then BC = 15+x

2/24 = 15/(15+x)

1/12 = 15/(15+x)

15+x = 15(12)

15+x = 180

x = 165

BC = 165+15 ==> 180 cm

Length of base of ramp = √(180 2 +24 2 )

= √(32400 +576 )

= √32976

= 181.59 cm

Approximately 1.81 m.

So, length of the base of ramp is 1.81 m.

Example 2 :

A boy who is 1.6 m tall casts a 2.4 m shadow when he stands 8.1 m from the base of an electric light pole. How high above the ground is the light globe ?

<DCE = <ACB (A)

1.6/x = 2.4/(2.4+8.1)

1.6/x = 2.4/10.5

1.6(10.5) = 2.4x

x = 16.8/2.4

x = 7

So, height of the light globe is 7 m.

Example 3 :

A piece of timber leaning against a wall, just touches the top of a fence, as shown. Find how far up the wall the timber reaches.

1.6/AB = 3/(3+2)

1.6/AB = 3/5

1.6(5) = 3AB

AB = 8/3

AB = 2.66 m

At 2.66 m above the timber reaches the wall.

Example 4 :

At the same time as the shadow cast by a vertical 30 cm long ruler is 45 cm long, Rafael’s shadow is 264 cm long.

a) Draw a fully labelled sketch of the situation.

b) Find Rafael’s height ?

(b) Rafael’s height AB = x m,

DE = 30 cm, BC = 264 cm and EC = 45 cm

Then, DE/AB = EC/BC

30/x = 45/264

45x = 7920

x = 7920/45

x = 176 cm

x = 176/100 m

x = 1.76 m

So, Rafael’s height is 1.76 m

Example 5 :

A 3.5 m ladder leans on a 2.4 m high fence. One end is on the ground and the other end touches a vertical wall 2.9 m from the ground. How far is the bottom of the ladder from the fence ?

∆DEC ~ ∆ABC using AA theorem.

AB = 2.9 m, AC = 3.5 m and CE = x cm

By using Pythagorean theorem,

AC 2 = AB 2 +BC 2

(3.5) 2 = (2.9) 2 +BC 2

BC 2 = 12.25 - 8.41

BC 2 = 3.84

BC = 1.95

DE = 2.4 cm

In similar triangles corresponding sides will be in same ratio.

2.4/2.9 = x/1.95

2.9x = 4.68

x = 1.62 m

So, the bottom of the ladder from the fence is ≈ 1.62 m

Example 6 :

Two surveyors estimate the height of a nearby mill. One stands 5 m away from the other on horizontal ground holding a 3 m stick vertically. The other surveyor finds a “line of sight” to the top of the hill, and observes this line passes the vertical stick at 2.4 m. They measures the distance from the stick to the top of the hill to be 1500 m using laser equipment. How high, correct to the nearest meter, is their estimate of the height of the hill ?

DE = 2.4 m, EC = 5 m, AB = x cm

CD/AC = CE/BC = DE/AB

CD 2 = CE 2 +DE 2

CD 2 = 5 2 +(2.4) 2

CD 2 = 25 +5.76

CD 2 = 30.76

CD = 5.5

CD/CA = DE/AB = CE/BC

5.5/1505.5 = 2.4/x = 5/(5+BE)

5.5/1505.5 = 2.4/x

5.5x = 2.4(1505.5)

x = 3613.2/5.5

x = 656

So, the height of the hill is ≈ 656 m.

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## Similar Triangles Worksheets

Explore this multitude of printable similar triangles worksheets for grade 8 and high school students; featuring exercises on identifying similar triangles, determining the scale factors of similar triangles, calculating side lengths of triangles, writing the similarity statements; finding similarity based on SSS, SAS and AA theorems, solving algebraic expressions to find the side length and comprehending similarity of right triangles and more. Make headway with our free similar triangles worksheets!

Check for Similar Triangles

Each 8th grade worksheet of this compilation comprises eight triangle pairs with indicated side lengths. Determine whether the triangles are similar by checking if their corresponding sides are proportional and label them.

Scale Factor of Similar Triangles

Determine the scale factor by finding the corresponding sides and writing their ratio. Find the scale factor of the bigger to the smaller triangle or vice versa in Part A and in Part B find both the scale factors.

Find the Sides of the Triangles using the Scale Factor

Offered in this set of pdf worksheets are the scale factors and side lengths of one of the similar triangles. Equate the ratio of the sides with the corresponding scale factors to determine the side lengths of the triangles.

Write the Similarity Statement | Level 1

Compare the similar triangles and complete the similarity statements, using the SSS criterion. Identify the proportional pairs of sides and rearrange the vertices based on the triangle given in the statement.

Write the Similarity Statement | Level 2

Bolster skills in writing the similarity statement with these printable worksheets. Figure out the proportional sides of the rotated similar triangles using the scale factor and name the triangles accordingly.

Similar Triangles | SSS, SAS and AA | Type 1

Observe the triangle pairs and based on the proportionality of their sides and congruence of their angles, identify the similarity postulates SSS, SAS, or AA and complete the similarity statements.

Similar Triangles | SSS, SAS and AA | Type 2

The triangles in this batch of similarity worksheets are either overlapped or combined. Decompose the triangles and identify the similarity criterion to complete the similarity statement in this array of high school worksheets.

Similar Triangles | Find the Sides | Type 1

Form an equation using the SSS criterion. Equate the ratios of two proportional pairs of sides in Part A and three proportional pairs of sides in Part B to find the missing lengths and sum up the side lengths to find the perimeter in Part C.

Similar Triangles | Find the Sides | Type 2

Level up with this bundle of worksheets featuring overlapping similar triangles. Analyze the flips and rotations, decompose the triangles and find their scale factor to figure out the indicated length(s).

Algebra in Similar Triangles | Solve for 'x' | Type 1

Each pair of triangles offered in this worksheet compilation is similar. Plug in the corresponding side length expressed as an algebraic expression in the similarity ratio and solve for 'x'.

Algebra in Similar Triangles | Solve for 'x' | Type 2

The similar triangles in this set of printable PDFs have common sides and vertices and involve side lengths presented as linear equations. Equate the ratios of the corresponding sides of the two triangles and simplify the equation to solve for 'x'.

Right Triangle Similarity

Conceptualize the right triangle similarity theorem with this collection of high school similar triangles worksheets. Write the similarity ratio of the right triangles using the known values to find the indicated length(s).

Related Worksheets

» Congruent Triangles

» Pythagorean Inequality Theorem

» Triangle Inequality Theorem

» Medians and Centroid of Triangles

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## Similar Triangles Worksheets

The similarity of triangles, like their congruency, is an important concept of geometry. Click on the below images to test yourself on the properties of similar triangles.

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## Right Similar Triangles Worksheet and Answer Key

Students will practice solving for side lengths of right similar triangles .

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## Similar Triangles by ECSDM

Grade levels.

Commencement, 10th Grade

## Learning Objectives

Using the PowerPoint lesson the students will:

- Learn how to set up a proportion using the given sides of a triangle and solve for the missing side.
- Draw a diagram form the given word problem and solve for the missing piece of information.
- Complete the accompanying worksheet for homework.

## Step-by-Step Procedures

- Slide 1 - Do now. Have students complete.
- Slide 2 - Notes on determining which side is similar and proportions.
- Slide 3 - Finding the similar side.
- Slide 4 - Examples where you find the missing side with the class.
- Slide 5 - Examples for the class to try.
- Slide 1 - Do now. Have students complete. When finished, go over homework.
- Slide 2 - Example of a word problem. Teacher guides students through while listing the steps to solve the problem.
- Slide 3 - Two examples for the students to be assisted through.
- Slide 4 - Three examples for the students to try independantly. Go over these problems in class.

## Description

This lesson covers similar triangles. Students will use proportions to solve for the missing side of a similar triangle. This lesson is suitable for the Math A curriculum.

Two 45-Minute periods

- SMART Board
- LCD Projector
- Similar Triangles Day 1 Worksheet
- Similar Triangle Word Problems Day 2 PowerPoint
- Similar Triangle Day 1 PowerPoint
- Similar Triangle Word Problem Day 2 Worksheet

## Assessments

Sudents will be informally assessed during the Do Now of day 2, as well as, with each homework assignment. The homework assignments are the worksheets listed in the materials section. The students will be expected to have 75% correct on each assignment.

## Related Academic Standards

New york state.

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

G-CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

## Similar Triangles Examples and Problems with Solutions

Definitions and theorems related to similar triangles are discussed using examples. Also examples and problems with detailed solutions are included.

## Worksheet 4.5 Word Problems involving similar triangles

## amycaballero_2020

similar triangles

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## Similar Triangles Word Problems

Similar Triangles Word Problems - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Similar triangles word problems, Similar triangles packet, Similar triangles and ratios, Similar triangles f12, Similar triangle applications, Similar triangles, Similar triangles date period, Similar right triangles.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

## 1. Similar Triangles Word Problems

2. similar triangles packet, 3. similar triangles and ratios, 4. similar triangles (f12), 5. 6.5 similar triangle applications, 6. similar triangles, 7. similar triangles date period -, 8. similar right triangles.

## Similar Triangles Word Problems Worksheets With Answers

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Similar Triangles Word Problem 2 - YouTube

Triangles discountpapers Similar triangles word problem 2 Worksheet on similar triangles

## Solving simple similar triangles word problem

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## Quiz b (13 to 18) solving with similar triangles, word problems

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Congruent triangles worksheet with answerSimilar right triangles worksheet answer key Problems word geometry solve worksheet triangles similar mathSimilar triangles worksheets.

## Similar triangles worksheets

Similar triangles example problemTriangles problems similar solving using applied math gr Similar triangles worksheet answers pdf11 10th grade geometry worksheets / worksheeto.com.

River triangles word similarSimilar triangles worksheet questions practice solution onlinemath4all Right triangle word problems worksheet — db-excel.comAngles answers triangles.

## Similar triangles practice worksheet answers

Similar and congruent triangles worksheet pdf / using similar polygonsProblems word similar triangles Triangles word problemsIdentifying similar triangles worksheet for 10th grade.

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## Right triangle word problems worksheet

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## 36 similar triangles worksheet answers

Problems similar word triangles answers triangle similarity worksheets geometryWord similar problems triangles example Similar triangles word problem : the casting shadowSolving similar triangles word problem with river.

Triangles practice .

Similar And Congruent Triangles Worksheet Pdf / Using Similar Polygons

Similar Triangles Word Problems Example 2 - YouTube

Similar Triangles Word Problems Example 1 - YouTube

Solving Simple Similar Triangles Word Problem - YouTube

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## IMAGES

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Solution Problem 2 : A boy who is 1.6 m tall casts a 2.4 m shadow when he stands 8.1 m from the base of an electric light pole. How high above the ground is the light globe ? Solution Problem 3 : A piece of timber leaning against a wall, just touches the top of a fence, as shown. Find how far up the wall the timber reaches. Solution Problem 4 :

Solution : In ∆DEC and ∆ABC, <DCE = <ACB (A) <DEC = <ABC (A) Using AA theorem, the above triangles ∆DEC ~ ∆ABC DE/AB = CD/CA = CE/BC DE/AB = CE/BC 1.6/x = 2.4/ (2.4+8.1) 1.6/x = 2.4/10.5 1.6 (10.5) = 2.4x

The following right triangles are similar. We will determine the unknown side lengths by using ratios within the first triangle. For each of the triangles below we define the base as the horizontal length of the triangle and the height as the vertical length.

ÐÏ à¡± á> þÿ þÿÿÿ ...

Solving Word Problems Involving Similar Triangles Geometry Skills Practice 1. A tree casts a shadow that is 18 ft long. Zachariah who is 5.5 ft tall casts a shadow that is 4.5 ft long. How tall...

61B Vocabulary Things to remember when figures are similar: 1) ONLY the angles are congruent 2) Side lengths are proportional Circle all the true statements regarding the similar figures represented below. Similar Figures Steps to determine if two figures are similar:

Now you are ready to create your Geometry Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Geometry Worksheet will produce eight problems for working with similar triangles. You may select whether to include non-similar triangle pairs, as well as the type of similarity in each pair.

Answers and explanations. 124. If two triangles are similar, their sides are in proportion. Suppose you call the original triangle A and the new triangle B. The proportion would be as follows: 3. A line that intersects two sides of a triangle and is parallel to the third side of the triangle creates two similar triangles.

Write the Similarity Statement | Level 1 Compare the similar triangles and complete the similarity statements, using the SSS criterion. Identify the proportional pairs of sides and rearrange the vertices based on the triangle given in the statement. Write the Similarity Statement | Level 2

College. Students use the properties of similar triangles to find the missing side lengths of triangles in a variety of word problems. The word problems involve shadows, mirrors, projections, and so on. We help you determine the exact lessons you need. We provide you thorough instruction of every step. We`re by your side as you try problems ...

360 cm 6. A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower? (draw a diagram and solve) 7. Triangles IJK and TUV are similar. The length of the sides of IJK are 40, 50, and 24.

Similar Triangles Worksheets Tags: 5th Grade 6th Grade The similarity of triangles, like their congruency, is an important concept of geometry. Click on the below images to test yourself on the properties of similar triangles. Download PDF Download PDF Download PDF Download PDF Download PDF Download PDF Download PDF Download PDF

These Similarity Worksheets will produce eight problems for working with similar triangles. You may select whether to include non-similar triangle pairs, as well as the type of similarity in each pair. These worksheets are a great resources for the 5th, 6th Grade, 7th Grade, 8th Grade, 9th Grade, and 10th Grade. Similar Right Triangles Worksheets.

Video Tutorial (You Tube Style) on right similar triangles. Free worksheet (pdf) and answer key on solving for side lenghts of right similar triangles. 29 scaffolded shet that start relatively easy and end with some real challenges.

Examples of solving problems using similar triangles. Example 1: Fred needs to know how wide a river is. He takes measurements as per the diagram at the right. Determine the river;s width. Example 2: Determine the ratio of the areas of the two similar triangles. Example 3: If the area of the smaller triangle is 20 m 2, determine the area of the ...

High school geometry > Similarity > Solving similar triangles Solve similar triangles (basic) VA.Math: 7.5 Google Classroom You might need: Calculator Triangle A B C is similar to triangle X Y Z . Solve for t . t = A C B 19.5 12 13.5 X Z Y t 4 4.5 Show Calculator Stuck? Review related articles/videos or use a hint. Do 4 problems

Geometry Worksheet Answer Page. Now you are ready to create your Geometry Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Geometry Worksheet will produce eight problems for working with similar right triangles. You may select the types of side lengths used in each problem.

Geometry Unit 9 - Solve Similar Triangles and Word Problems Worksheet. by. Plain and Simple Geometry. 3. $1.99. PDF. Solve Similar Triangles and Word Problems Worksheet Using similar triangles find the length of a side or perimeter. Includes word problems and special properties of similar parts with parallel lines.

Examples, solutions, videos, worksheets, stories, and lessons to help Grade 8 students learn about solving problems using similar triangles. How to solve problems that involve similar triangles? 1. Sketch a diagram of the problem, identifying the similar triangles. 2. Set up the proportion. 3. Cross multiply. 4. Divide.

Similar Triangle Word Problem Day 2 Worksheet; Assessments. Sudents will be informally assessed during the Do Now of day 2, as well as, with each homework assignment. The homework assignments are the worksheets listed in the materials section. The students will be expected to have 75% correct on each assignment.

Two triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows. AB / A'B' = BC / B'C' = CA / C'A' Angle-Angle (AA) Similarity Theorem

Worksheet 4.5 Word Problems involving similar triangles Worksheet 4.5 Word Problems involving similar triangles. amycaballero_2020 Member for 2 years 2 months Age: 14-18. Level: 9. Language: English (en) ID: 1308516. 25/08/2021. Country code: TH. Country: Thailand. School ...

Similar Triangles Word Problems - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Similar triangles word problems, Similar triangles packet, Similar triangles and ratios, Similar triangles f12, Similar triangle applications, Similar triangles, Similar triangles date period, Similar right triangles.

Similar right triangles worksheet answersSimilar triangles word problems example 1 Similar triangles with shadows similar triangles, word problems, dominoTrigonometry worksheet triangle answers right problems trig word triangles worksheets similar geometry math bearings problem resourceaholic don teaching steward solving.