Answer to Question #251219 in Geometry for sophia

Question

Provide the missing statement and reasons for the following proof:

Given: <BDA ~= <A

Prove:  x=3

statement reason

S1. <BDA ~= <A R1. Given

S2. <BDA ~= <CDE R2.

S3. <CDE ~= <A R3. Transitive Property of Congruence

S4. m<CDE = m<A R4.

S5. R5. Substitution Property of Equality

S6. 14x = 13x + 3 R6.

S7. x = 3 R7. Subtraction Property of Equality

Answer 1

We are given that;

$\angle BDA \widetilde{=}\angle A$

we want to prove that; x=3

statement 1; $\angle BDA \widetilde{=}\angle A$

Reason; it is given

statement 2; $\angle BDA \widetilde{=}\angle CDE;$

The statement means they are congruent and equal.

Reason; vertically opposite angles are equal

statement 3; $\angle CDE \widetilde{=} \angle A;$

This means $\angle CDE$ is congruent to $\angle A$

Reason; Transitive property of congruence.

statement 4;

$m<CDE=m\angle A.$

We saw that $\angle BDA \widetilde{=} \angle A \space and \space \angle BDA\widetilde{=}\angle CDE.$

Thus, by Reason; transitive property of equality.