Certainly! Here are 10 detailed questions on the chapter of similar triangles, complete with variables and numbers.
1. Ratio of Sides
If triangle ABC is similar to triangle DEF, and side AB = 4x + 2, DE = 2x + 6, find the value of x if the ratio of sides is 2:1.
2. Area Ratios
Two similar triangles have side lengths in the ratio of 3:5. What is the ratio of their areas?
3. Height Calculation
In triangle PQR, angle P = angle R, and PQ = 3y + 4. If QR = 8 and PR = 2y + 6, find y.
4. Corresponding Angles
If triangle GHI is similar to triangle JKL, and angle G = 50°, what is the measure of angle J?
5. Perimeter Problem
The perimeter of triangle MNO is 36 cm, and triangle PQR is similar to triangle MNO with a scale factor of 2. What is the perimeter of triangle PQR?
6. Finding Missing Lengths
If triangle ABC is similar to triangle XYZ, and AB = 5, AC = 12, and XY = 10, find the length of XZ.
7. Scale Factor
If triangle DEF is similar to triangle GHI and the scale factor is 3:4, if the length of DE = 12, what is the length of GH?
8. Height Ratios
In similar triangles, if the height from vertex A to side BC is 6 cm, what is the height from vertex D to side EF if the ratio of the sides is 5:3?
9. Shadow Problem
A 2m tall tree casts a shadow of 4m. If a person 1.6m tall stands close by and casts a shadow of x meters, find x.
10. Finding Unknown Angles
If triangle JKL is similar to triangle MNO, and angle K = 70°, what is the measure of angle N?
These questions cover various aspects of similar triangles, including ratios, area, perimeter, and angles, providing a comprehensive understanding of the topic.