Question #251219

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


1
Expert's answer
2021-10-19T17:38:01-0400

We are given that;

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

we want to prove that; x=3

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

Reason; it is given

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

The statement means they are congruent and equal.

Reason; vertically opposite angles are equal

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

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

Reason; Transitive property of congruence.

statement 4;

m<CDE=mA.m<CDE=m\angle A.

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

Thus, by Reason; transitive property of equality.


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