This document discusses the right triangle similarity theorem and provides examples of its application. The theorem states that if an altitude is drawn to the hypotenuse of a right triangle, the two new triangles formed are similar to each other and the original triangle. Several examples demonstrate using the theorem to find missing side lengths by setting up proportions between corresponding sides of similar triangles.

2. LEARNING COMPETENCY
prove the conditions for similarity of right triangles.
M9GE-IIIg-h-1
LEARNING OBJECTIVES:
1. State the Right Triangle Similarity Theorem
2. Illustrate the Right Triangle Similarity Theorem
3. Apply the Right Triangle Similarity Theorem to find the missing
sides.
OBJECTIVES

3. If the altitude of a right triangle is
drawn to the hypotenuse, then the
two triangles formed are similar with
each other and to the original right
triangle.
Right Triangle Similarity Theorem

4. ઢࢄࢅࢆ∼ઢࢄࢃࢅ∼ઢࢅࢃࢆ

5. Δ𝐽𝐾𝑀∼Δ𝐽𝐿𝐾∼Δ𝐾𝐿𝑀

6. Δ𝑃𝑄𝑅∼Δ𝑃𝑆𝑄∼Δ𝑄𝑆𝑅

7. Δ𝐴𝐵𝐶∼Δ𝐶𝐵𝐷∼Δ𝐴𝐶𝐷

8. EXAMPLE 1: Find FG
𝐹𝐺
𝐸𝐺
=
𝐻𝐺
𝐹𝐺
𝐹𝐺
9
=
3
𝐹𝐺
𝐹𝐺 𝐹𝐺 = (3)(9)
𝐹𝐺 2
= 27
𝐹𝐺 2 = 27
𝐹𝐺 = 3 3

9. EXAMPLE 2
𝑥
6
=
6 + 8
𝑥
𝑥
6
=
14
𝑥
𝑥 𝑥 = (6)(14)
𝑥 2
= 84
𝑥 2 = 84
𝑥 = 2 21

10. EXAMPLE 2
𝑦
6
=
8
𝑦
𝑦 𝑦 = (6)(8)
𝑦 2 = 48
𝑦 2 = 48
𝑦 = 4 3

11. EXAMPLE 2
𝑧
8
=
6 + 8
𝑧
𝑧
8
=
14
𝑧
𝑧 𝑧 = (8)(14)
𝑧 2
= 112
𝑧 2 = 112
𝑧 = 4 7

12. X
45 X
81
𝑥
45
=
81
𝑥
𝑥 𝑥 = (45)(81)
𝑥2 = 3645
𝑥2 = 3645
𝑥 = 27 5

13. X
9 X
7
𝑥
9
=
7
𝑥
𝑥 𝑥 = (9)(7)
𝑥2 = 63
𝑥2 = 63
𝑥 = 3 7

14. X
84 X
16
𝑥
84
=
16
𝑥
𝑥 𝑥 = (84)(16)
𝑥2 = 1344
𝑥2 = 1344
𝑥 = 8 21

15. EVALUATION

17. 𝑥
36
=
100
𝑥
𝑥 𝑥 = (36)(100)
𝑥 2 = 3600
𝑥 = 3600
𝑥 = 60