Given: AC perpendicular BD and AB congruent CB. Prove AD congruent CD. It is a kite figure. I need statements and reasons. Problem states Plan: prove triangle ABE congruent CBE. The use congruent corresponding parts AE and CE to show right triangle AED congruent CED. AD and CD will then be congruent corresponding parts.
So, did you
use congruent corresponding parts AE and CE to show right triangle AED congruent CED
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To prove that AD is congruent to CD in a kite figure where AC is perpendicular to BD and AB is congruent to CB, you can follow these statements and reasons:
1. Given: AC is perpendicular to BD (Given)
2. Given: AB is congruent to CB (Given)
3. Plan: To prove triangle ABE is congruent to CBE (Plan)
4. Statement: Angle ABE is congruent to angle CBE (Kite Property)
Reason: In a kite, the angles between the congruent sides are congruent.
5. Statement: Angle BAE is congruent to angle BCE (Kite Property)
Reason: In a kite, the angles between the congruent sides are congruent.
6. Statement: AB is congruent to CB (Given)
Reason: Given information.
7. Statement: Triangle ABE is congruent to triangle CBE (Angle-Side-Angle congruence theorem)
Reason: By combining statements 4, 5, and 6, we have enough information to prove the congruence of the triangles.
8. Statement: AE is congruent to CE (Corresponding parts of congruent triangles are congruent)
Reason: In congruent triangles, corresponding sides are congruent.
9. Statement: Triangle AED is congruent to triangle CED (Side-Angle-Side congruence theorem)
Reason: By combining statements 7 and 8, we have enough information to prove the congruence of the triangles.
10. Statement: AD is congruent to CD (Corresponding parts of congruent triangles are congruent)
Reason: In congruent triangles, corresponding sides are congruent.
Therefore, we have proven that AD is congruent to CD in the given kite figure using the plan provided.