Answer to Question #251219 in Geometry for sophia

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

Expert's answer

We are given that;

we want to prove that; x=3

statement 1;

Reason; it is given

statement 2;

The statement means they are congruent and equal.

Reason; vertically opposite angles are equal

statement 3;

This means is congruent to

Reason; Transitive property of congruence.

statement 4;

We saw that

Thus, by Reason; transitive property of equality.

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