MathematicsGrade 9en

📐 Similar Triangles and Proportional Reasoning

This quiz covers the fundamentals of similar triangles, proportional sides, and scaling relationships in geometry. **What you'll learn:** - Identify similar triangles using angle and side criteria - Set up and solve proportions from similar figures - Apply scale factors to find missing side lengths - Use similar triangles to solve real-world measurement problems - Understand the relationship between corresponding sides in scaled figures

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Questions in this quiz

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Question 1
Two triangles are similar if their corresponding angles are equal. Which of the following is NOT a correct criterion for triangle similarity?
Question 2
If triangle $ABC$ is similar to triangle $DEF$ , then the ratio of their corresponding sides must be equal.
Question 3
Triangle $PQR$ has sides of length $3$ cm, $4$ cm, and $5$ cm. Triangle $XYZ$ is similar to triangle $PQR$ with a scale factor of $2$ . What is the length of the side in triangle $XYZ$ that corresponds to the $4$ cm side?
Question 4
Triangle $ABC$ has sides $6$ cm, $8$ cm, and $10$ cm. Triangle $DEF$ is similar with sides $3$ cm, $4$ cm, and ___. The scale factor from triangle $ABC$ to triangle $DEF$ is ___.
Question 5
If two triangles have the same perimeter, they must be similar.
Question 6
In similar triangles $MNO$ and $PQR$ , side $MN = 12$ cm and the corresponding side $PQ = 9$ cm. If side $NO = 16$ cm, what is the length of the corresponding side $QR$ ?
Question 7
Two similar rectangles have a scale factor of $3:2$ . If the larger rectangle has a width of $15$ cm, the width of the smaller rectangle is ___.
Question 8
A telephone pole casts a shadow of $8$ metres. At the same time, a $2$ metre tall person standing nearby casts a shadow of $1.5$ metres. Using similar triangles, how tall is the telephone pole?
Question 9
Two triangles with all corresponding sides in the ratio $2:3$ must be similar.
Question 10
Triangle $ABC$ is similar to triangle $DEF$ . The ratio of corresponding sides is $5:3$ . If the area of triangle $ABC$ is $100$ square cm, what is the area of triangle $DEF$ ?