Which theorem can you use to prove the two triangles are similar? The image depicts two nested right-angled triangles labeled as follows:1. The larger triangle is ∆HJK with vertices at points H, J, and K.2. The smaller triangle is ∆RST with vertices at points R, S, and T. The smaller triangle lies within the larger triangle, sharing the right angle at point T.Key dimensions and angles are labeled:- In the larger triangle ∆HJK: - The hypotenuse HJ is 10 units. - The leg JK is 8 units. - The leg HT is unlabeled.- In the smaller triangle ∆RST: - The hypotenuse RS is 6 units. - The leg ST is 4.8 units. - The leg RT is unlabeled.Additionally, the diagram indicates that the angles ∠HTK and ∠JST are equal, suggesting a similarity between the two triangles.This detailed breakdown of the geometric figure is used to illustrate the concept of similar triangles and their properties, particularly focusing on the proportionality of the corresponding sides and angles. This can be useful in an educational setting to apply and understand the properties of similar triangles and theorems related to right-angle triangles.

Answered: Image /qna-images/answer/33bae9cd-b35e-440a-a643-4b6b2727d3d9.jpg

Answered: theorems we learr H R 10 6 4.8 8

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Which theorem can you use to prove the two triangles are similar?

The image depicts two nested right-angled triangles labeled as follows:

1. The larger triangle is ∆HJK with vertices at points H, J, and K.
2. The smaller triangle is ∆RST with vertices at points R, S, and T. The smaller triangle lies within the larger triangle, sharing the right angle at point T.

Key dimensions and angles are labeled:
- In the larger triangle ∆HJK:
- The hypotenuse HJ is 10 units.
- The leg JK is 8 units.
- The leg HT is unlabeled.

- In the smaller triangle ∆RST:
- The hypotenuse RS is 6 units.
- The leg ST is 4.8 units.
- The leg RT is unlabeled.

Additionally, the diagram indicates that the angles ∠HTK and ∠JST are equal, suggesting a similarity between the two triangles.

This detailed breakdown of the geometric figure is used to illustrate the concept of similar triangles and their properties, particularly focusing on the proportionality of the corresponding sides and angles. This can be useful in an educational setting to apply and understand the properties of similar triangles and theorems related to right-angle triangles.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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