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 )
= 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).
» 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 .
This is a 4 part worksheet:
- Part I Model Problems
- Part II Practice
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- Part IV Answer Key
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Similar Triangles by ECSDM
Commencement, 10th Grade
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.
- 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.
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
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
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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.
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