Lesson 3
Scaled Relationships
Problem 1
Here is Quadrilateral \(ABCD\).
![Quadrilateral ABCD is on a grid.](https://cms-im.s3.amazonaws.com/iNwd9oUU8CeHiBnW4T3iCWta?response-content-disposition=inline%3B%20filename%3D%227-7.1.PP.New.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.PP.New.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=68296e8a5949983c7585b28cd4b7fc95451703bfa324fe29e0915837cb6d6b1f)
Quadrilateral \(PQRS\) is a scaled copy of Quadrilateral \(ABCD\). Point \(P\) corresponds to \(A\), \(Q\) to \(B\), \(R\) to \(C\), and \(S\) to \(D\).
If the distance from \(P\) to \(R\) is 3 units, what is the distance from \(Q\) to \(S\)? 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 2
Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.
![Four rectangles, labeled P, Q, R and S.](https://cms-im.s3.amazonaws.com/r92sCFtwgkGK3qLKRXxxY76s?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.22.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=91fe4bd84f7ec3523c2cbcde158ed5bf5a34ef2fb0425c0afe7807dc2d45902c)
- from P to Q
- from P to R
- from Q to S
- from Q to R
- from S to P
- from R to P
- from P to S
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 3
Triangle S and Triangle L are scaled copies of one another.
-
What is the scale factor from S to L?
-
What is the scale factor from L to S?
-
Triangle M is also a scaled copy of S. The scale factor from S to M is \(\frac{3}{2}\). What is the scale factor from M to S?
![Two triangles labeled S and L on a grid. Triangle S has a horizontal base of 2 units and a height of 4 units. Triangle L has a horizontal base of 4 units and a height of 8 units.](https://cms-im.s3.amazonaws.com/QzSG8Ti4pi8B684RjAQQEcZQ?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.31.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.31.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=12c239fc97ee5a32fbfd3a4fb55cb6cb942b1640ceb0e4331643b1fb532dcaed)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 4
Are two squares with the same side lengths scaled copies of one another? 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 5
Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other? Explain.
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 2.)Problem 6
The line has been partitioned into three angles.
![A straight line with two rays coming out of a single point.](https://cms-im.s3.amazonaws.com/dc5os7EpTNp9H4DanFhYwXFt?response-content-disposition=inline%3B%20filename%3D%228-8.1.D.PP.Image.04.5.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D.PP.Image.04.5.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000400Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d96f94b182721a05ce1d734e8c4380c376590a4854b2086ab842cea13981c710)
Is there a triangle with these three angle measures? Explain.
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 13.)