http://www.ck12.org Chapter 4. Triangles and Congruence
- Fill in the blanks in the proof below.
Given:
AB∼=DC,BE∼=CE
Prove: 4 ABE∼= 4 ACE
TABLE4.8:
Statement Reason
- 2.^6 AEB∼=^6 DEC 2.
- 4 ABE∼= 4 ACE 3.
Answers:
The pair of triangles is congruent by the SAS postulate. 4 CAB∼= 4 QRS.
We know that one pair of sides and one pair of angles are congruent from the diagram. In order to know that the
triangles are congruent by SAS we need to know that the pair of sides on the other side of the angle are congruent.
So, we need to know thatEF∼=BA.
TABLE4.9:
Statement Reason
1.AB∼=DC,BE∼=CE 1. Given2.^6 AEB∼=^6 DEC 2. Vertical Angle Theorem
3. 4 ABE∼= 4 ACE 3. SAS postulate
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Are the pairs of triangles congruent? If so, write the congruence statement and why.