Question

Would the diagram prove angle ABC and angle EDC be a side angle side?

Answer 1

Using the diagram, we must prove that △ABC ≅ △EDC.

1)

• Statement: ,AC ≅ EC

,

• Reason: ,Given,. From the diagram, we see that the sides are congruent.

2)

• Statement: ,DC ≅ BC

,

• Reason: ,Given,. From the diagram, we see that the sides are congruent.

3)

• Statement: ,∠ACB ≅ ∠DCE

,

• Reason: ,Vertical angles ,(Theorem, when two straight lines intersect, they form two sets of linear pairs with congruent angles).

4)

• Statement: ,△ABC ≅ △EDC

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• Reason: ,SAS Theorem ,(If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent).

Answer

13. Statement: ∠ACB ≅ ∠DCE

14. Reason: SAS Theorem