Students were asked over to answer a question at schools and to indicate what is most important for them to succeed. One that response stood out from the rest was practice. Successful persons commonly are not born successful; they become successful through hard work and perseverance. If you would like to accomplish your goals, keep this in mind! as follows some question and answer examples that you will be able to utilize to develop your knowledge and gain insight that will assist you to continue your school studies.

## Question:

Unit 8 right triangles and trigonometry homework 3 similar right triangles and geometric mean

## Answer:

The** right triangles** that have an altitude which **forms **two right triangles

are similar to the two right triangles formed.

**Responses**:

1. ΔLJK ~ ΔKJM

ΔLJK ~ ΔLKM

ΔKJM ~ ΔLKM

2. ΔYWZ ~ ΔZWX

ΔYWZ ~ ΔYZW

ΔZWX ~ ΔYZW

3. x = __4.8__

4. x ≈ __14.48__

5. x ≈ __11.37__

6. G.M. = __12·√3__

7. G.M. = __6·√5__

### What condition guarantees the similarity of the right triangles?

1. **∠LMK **= 90° given

∠JMK + ∠LMK =** 180° linear pair **angles

**∠JMK** = 180° – 90° = 90°

**∠JKL** ≅ ∠JMK** **All 90° angles are congruent

∠LJK ≅** ∠LJK reflexive property**

__ΔLJK is similar to ΔKJM__by Angle–Angle, AA, similarity postulate

∠JLK ≅ ∠JLK by **reflexive property**

__ΔLJK is similar to ΔLKM__by AA similarity

By the property of **equality **for triangles that have equal **interior angles**, we have;

__ΔKJM ~ ΔLKM__

2. ∠YWZ ≅ **∠YWZ **by reflexive property

∠WXZ ≅ **∠YZW **all 90° angle are congruent

__ΔYWZ is similar to ΔZWX__, by AA similarity postulate

**∠XYZ **≅ ∠WYZ by reflexive property

**∠YXZ **≅ ∠YZW all 90° are congruent

__ΔYWZ is similar to ΔYZW__by AA similarity postulate

Therefore;

__ΔZWX ~ ΔYZW__

3. The **ratio **of **corresponding sides **in **similar triangles **are equal

From the similar triangles, we have;

8 × 6 = **10 × x**

48 = 10·x

3. From the similar triangles, we have;

20 × 21 = **x × 29**

**420** = 29·x

4. From the similar triangles, we have;

20 × 48 = **52 × x**

5. From the similar triangles, we have;

13.2 × 22.4 = **26 × x**

6. The **geometric mean**, **G.M. **is **given **by the formula;

The geometric mean of** 16 **and **27 **is therefore;

- The geometric mean of 16
__12·√3__

7. The geometric mean of **5 **and** 36 **is found as follows;

- The geometric mean of 5 and 36 is
__6·√5__

Learn more about the **AA similarity postulate **and **geometric mean** here:

They could possibly hopefully help the student deal with the question by working with the questions and answer examples. You could simply then have a discussion with your classmate and continue the school learning by studying the subject altogether.