given $ \triangle wxy $ is isosceles with legs $ \overline { wx } $ and $ \overline { wy } $, $ \triangle wvz $ is isosceles with legs $ \overline { wv } $ and $ \overline { wz } $. prove $ \triangle wxy \sim \triangle wvz $.

complete the steps of the proof.

| statements | reasons |
| --- | --- |
| 1 $ \triangle wxy $ is isosceles with legs $ \overline { wx } $ and $ \overline { wy } $ | 1 given |
| 2 $ \triangle wvz $ is isosceles with legs $ \overline { wv } $ and $ \overline { wz } $ | 2 given |
| 3 $ \overline { wx } \cong \overline { wy } $, $ \overline { wv } \cong \overline { wz } $ | 3 def of isosceles triangle |
| 4 $ \diamond $ | 4 def of $ \cong $ |
| 5 $ ( wz ) ( wx ) = ( wy ) ( wz ) $ | 5. multiplication property |
| 6 $ ( wz ) ( wx ) = ( wy ) ( wv ) $ | 6 $ \diamond $ |
| 7 $ \frac { wy } { wz } = \frac { wx } { wv } $ | 7 property of proportion |
| 8 $ \angle w \cong \angle w $ | 8 reflexive property |
| 9 $ \triangle wxy \sim \triangle wvz $ | 9 $ \diamond $ |

sas similarity theorem
ssa similarity theorem
sss similarity theorem
ratio

Question

given $ \triangle wxy $ is isosceles with legs $ \overline { wx } $ and $ \overline { wy } $, $ \triangle wvz $ is isosceles with legs $ \overline { wv } $ and $ \overline { wz } $. prove $ \triangle wxy \sim \triangle wvz $.

complete the steps of the proof.

| statements | reasons |
| --- | --- |
| 1 $ \triangle wxy $ is isosceles with legs $ \overline { wx } $ and $ \overline { wy } $ | 1 given |
| 2 $ \triangle wvz $ is isosceles with legs $ \overline { wv } $ and $ \overline { wz } $ | 2 given |
| 3 $ \overline { wx } \cong \overline { wy } $, $ \overline { wv } \cong \overline { wz } $ | 3 def of isosceles triangle |
| 4 $ \diamond $ | 4 def of $ \cong $ |
| 5 $ ( wz ) ( wx ) = ( wy ) ( wz ) $ | 5. multiplication property |
| 6 $ ( wz ) ( wx ) = ( wy ) ( wv ) $ | 6 $ \diamond $ |
| 7 $ \frac { wy } { wz } = \frac { wx } { wv } $ | 7 property of proportion |
| 8 $ \angle w \cong \angle w $ | 8 reflexive property |
| 9 $ \triangle wxy \sim \triangle wvz $ | 9 $ \diamond $ |

sas similarity theorem
ssa similarity theorem
sss similarity theorem
ratio

Accepted Answer

# Explanation:
## Step1: Definition of congruent segments
Since $ \overline{WX}\cong\overline{WY}$ and $ \overline{WV}\cong\overline{WZ}$, by the definition of congruent segments $ WX = WY$ and $ WV=WZ$.
## Step2: Substitution property
In step 5, we have $(WZ)(WX)=(WY)(WZ)$. Since $ WV = WZ$ (from step 3), we can substitute $ WZ$ with $ WV$ in the right - hand side of the equation. So, $(WZ)(WX)=(WY)(WV)$ (by substitution property).
## Step3: SAS similarity theorem
We have $\frac{WY}{WZ}=\frac{WX}{WV}$ (from step 7) and $ \angle W\cong\angle W$ (reflexive property). By the Side - Angle - Side (SAS) similarity theorem, if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the two triangles are similar.

# Answer:
4. $ WX = WY$ and $ WV = WZ$
6. Substitution property ($ WZ = WV$)
9. SAS similarity theorem

statements	reasons
2 \\( \triangle wvz \\) is isosceles with legs \\( \overline { wv } \\) and \\( \overline { wz } \\)	2 given
3 \\( \overline { wx } \cong \overline { wy } \\), \\( \overline { wv } \cong \overline { wz } \\)	3 def of isosceles triangle
4 \\( \diamond \\)	4 def of \\( \cong \\)
5 \\( ( wz ) ( wx ) = ( wy ) ( wz ) \\)	5. multiplication property
6 \\( ( wz ) ( wx ) = ( wy ) ( wv ) \\)	6 \\( \diamond \\)
7 \\( \frac { wy } { wz } = \frac { wx } { wv } \\)	7 property of proportion
8 \\( \angle w \cong \angle w \\)	8 reflexive property
9 \\( \triangle wxy \sim \triangle wvz \\)	9 \\( \diamond \\)

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QUESTION IMAGE

Question

Explanation:

Step1: Definition of congruent segments

Step2: Substitution property

Step3: SAS similarity theorem

Answer: