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