Question

Fill in the missing statements and reasons in the proof.

Answer 1

through theorem SAS the triangles are congruent.

so <D=<A

other corresponding fearures of congruent pair of triangles

Explanation:

vetically opposite angles

<EBD=<ABC

Answer 2

`\angle EBD=\angle ABC` ( By vertical angles theorem)

`\triangle ABC\cong \triangle EBD` (By SAS postulate)

`\angle D\cong \angle A` (CPCT)

Explanation:

We are given that

Segment AB is congruent to segment DB and segment EB is congruent to segment to CB.

We have to prove that Angle D is congruent to angle A.

Triangle ABC and triangle EBD

`EB=CB`

`AB=DB`

`\angle EBD=\angle ABC` ( By vertical angles theorem)

`\triangle ABC\cong \triangle EBD` (By SAS postulate)

`\angle D\cong \angle A` (CPCT)

Hence, proved