Question
Given: $\overset{―}{B A} ≅ \overset{―}{D C}, \overset{―}{B A} ⊥ \overset{―}{A D}$ and $\overset{―}{A D} ⊥ \overset{―}{D C}$ .
Prove: $△ B A D ≅ △ C D A$ .
Step
1
try
Statement
$\overset{―}{B A} ≅ \overset{―}{D C}$
$\begin{array}{l} \overset{―}{B A} ⊥ \overset{―}{A D} \\ \overset{―}{A D} ⊥ \overset{―}{D C} \end{array}$

Reason

Given

Type of Statement

Answer

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Answer

Check: The triangles $△ B A D$ and $△ C D A$ are congruent, which meets the requirements of the problem

Steps

Step 1 ： $\overset{―}{B A} ≅ \overset{―}{D C}$ (Given)

Step 2 ： $\overset{―}{B A} ⊥ \overset{―}{A D}$ and $\overset{―}{A D} ⊥ \overset{―}{D C}$ (Given)

Step 3 ： $∠ B A D = ∠ C D A$ (Both are right angles, so they are congruent)

Step 4 ： $\overset{―}{A D} ≅ \overset{―}{A D}$ (Reflexive property of congruence)

Step 5 ： $△ B A D ≅ △ C D A$ (By the Hypotenuse-Leg (HL) Theorem, if a right triangle has a hypotenuse and a leg that are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent)

Step 6 ：Check: The triangles $△ B A D$ and $△ C D A$ are congruent, which meets the requirements of the problem

QuestionGiven: BA―≅DC―,BA―⊥AD― and AD―⊥DC―.Prove: △BAD≅△CDA.Step1tryStatementBA―≅DC―BA―⊥AD―AD―⊥DC― Reason Given Type of Statement

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