Lesson 8
Similar Triangles
Problem 1
In each pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not. Explain how you know.
-
Triangle A: 53, 71, ___; Triangle B: 53, 71, ___
-
Triangle C: 90, 37, ___; Triangle D: 90, 53, ___
-
Triangle E: 63, 45, ____; Triangle F: 14, 71, ____
-
Triangle G: 121, ___, ___; Triangle H: 70, ___, ___
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
-
Draw two equilateral triangles that are not congruent.
- Measure the side lengths and angles of your triangles. Are the two triangles similar?
-
Do you think two equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
In the figure, line \(BC\) is parallel to line \(DE\).
![Two triangles. First, A, B C. Then triangle A, D E where D lies on side A, B and E lies on side A, E.](https://cms-im.s3.amazonaws.com/Qhexj1cMRXNhDkvRaax6tphz?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.13.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.13.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T191744Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f269d642ce4359ff98a4a330ecc10a8b475bdaf6c74825f470e74b0ea59fe904)
Explain why \(\triangle ABC\) is similar to \(\triangle ADE\).
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 4
The quadrilateral \(PQRS\) in the diagram is a parallelogram. Let \(P’Q’R’S’\) be the image of \(PQRS\) after applying a dilation centered at a point O (not shown) with scale factor 3.
![Quadrilateral P Q R S on a square grid.](https://cms-im.s3.amazonaws.com/wmd3NdUusS4hd9qSy5RoCN8b?response-content-disposition=inline%3B%20filename%3D%228-8.2.A.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T191744Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14df4d912f644f5ac702e3f640a46440f3e28393d3a3bfe245c1f22aebe185e2)
Which of the following is true?
\(P’Q’= PQ\)
\(P’Q’=3PQ\)
\(PQ=3P’Q’\)
Cannot be determined from the information given
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 2, Lesson 4.)Problem 5
Describe a sequence of transformations for which Quadrilateral P is the image of Quadrilateral Q.
![Two quadrilaterals in an x y plane.](https://cms-im.s3.amazonaws.com/qBPDuyfnrmYr6yyg3hYGfSZq?response-content-disposition=inline%3B%20filename%3D%228-8.1.A6.newPP.03b.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A6.newPP.03b.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T191744Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4a53394406b0a5e7b38edb80838b5078ef67cabd9b173ddb408f86b70e6c483a)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 1, Lesson 6.)