digital textbook: click each link below to learn the concepts. each component includes a video and you can select your desired language. student fl geometry - triangle congruence - proving triangles congruent - 5.6.2 guided instruction student fl geometry - triangle congruence - proving triangles congruent - 5.6.3 guided practice then, answer check your understanding assignment below. you have three attempts. given: $ \overline { x h } \perp \overline { y v } $, $ \overline { y x } \cong \overline { v x } $ prove: $ \triangle v x h \cong \triangle y x h $ complete the paragraph proof. it is given that $ \overline { x h } \perp \overline { y v } $, so $ \angle v h x $ and $ \angle y h x $ are right angles by the. therefore, $ \triangle v x h $ and $ \triangle y x h $ are right triangles by the. it is also given that $ \overline { y x } \cong \overline { v x } $. $ \overline { h x } \cong \overline { h x } $ by the. therefore, $ \triangle v x h \cong \triangle y x h $ by

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digital textbook: click each link below to learn the concepts. each component includes a video and you can select your desired language. student fl geometry -> triangle congruence -> proving triangles congruent -> 5.6.2 guided instruction student fl geometry -> triangle congruence -> proving triangles congruent -> 5.6.3 guided practice then, answer check your understanding assignment below. you have three attempts. given: $ \overline { x h } \perp \overline { y v } $, $ \overline { y x } \cong \overline { v x } $ prove: $ \triangle v x h \cong \triangle y x h $ complete the paragraph proof. it is given that $ \overline { x h } \perp \overline { y v } $, so $ \angle v h x $ and $ \angle y h x $ are right angles by the. therefore, $ \triangle v x h $ and $ \triangle y x h $ are right triangles by the. it is also given that $ \overline { y x } \cong \overline { v x } $. $ \overline { h x } \cong \overline { h x } $ by the. therefore, $ \triangle v x h \cong \triangle y x h $ by

Accepted Answer

# Explanation:
## Step1: Definition of perpendicular lines
If two lines are perpendicular, the angle between them is $90^{\circ}$. So, if $\overline{XH}\perp\overline{YV}$, then $\angle VHX$ and $\angle YHX$ are right angles by the **definition of perpendicular lines**.
## Step2: Definition of right - triangle
A triangle with a right angle is a right - triangle. Since $\angle VHX$ and $\angle YHX$ are right angles, $\triangle VXH$ and $\triangle YXH$ are right triangles by the **definition of right - triangle**.
## Step3: Reflexive property of congruence
For any segment $a$, $a\cong a$. So, $\overline{HX}\cong\overline{HX}$ by the **reflexive property of congruence**.
## Step4: Hypotenuse - Leg (HL) congruence theorem
In right - triangles, if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. Here, $\overline{YX}\cong\overline{VX}$ (hypotenuse) and $\overline{HX}\cong\overline{HX}$ (common leg). So, $\triangle VXH\cong\triangle YXH$ by the **Hypotenuse - Leg (HL) congruence theorem**.

# Answer:
1. definition of perpendicular lines
2. definition of right - triangle
3. reflexive property of congruence
4. Hypotenuse - Leg (HL) congruence theorem

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QUESTION IMAGE

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Explanation:

Step1: Definition of perpendicular lines

Step2: Definition of right - triangle

Step3: Reflexive property of congruence

Step4: Hypotenuse - Leg (HL) congruence theorem

Answer: