Question

this is a 2 - page document!
state whether the triangles could be proven congruent, if possible, by sss or sas.
then, write a congruency statement. # 1 is done for you!
1.

3.

5.

2.

4.

6.

Explanation:

Step1: Identify congruent parts for problem 2

In \(\triangle BED\) and \(\triangle AEC\), \(BD = AC\) (given by marks), \(\angle BED=\angle AEC\) (vertical angles are equal), \(BE = AE\) (given by marks). So by SAS (Side - Angle - Side) criterion.

Step2: Write congruency statement for problem 2

\(\triangle BED\cong\triangle AEC\)

Step3: Identify congruent parts for problem 3

In \(\triangle VST\) and \(\triangle UST\), \(VT = UT\) (given by marks), \(\angle VTS=\angle UTS\) (given by marks), \(ST = ST\) (common side). So by SAS (Side - Angle - Side) criterion.

Step4: Write congruency statement for problem 3

\(\triangle VST\cong\triangle UST\)

Step5: Identify congruent parts for problem 4

In \(\triangle MNQ\) and \(\triangle PNQ\), \(MN = PN\) (given by marks), \(MQ = PQ\) (given by marks), \(NQ = NQ\) (common side). So by SSS (Side - Side - Side) criterion.

Step6: Write congruency statement for problem 4

\(\triangle MNQ\cong\triangle PNQ\)

Step7: Identify congruent parts for problem 5

In \(\triangle GIL\) and \(\triangle HKL\), \(GL = HL\) (given by marks), \(IL = KL\) (given by marks), \(\angle GL I=\angle HLK\) (vertical angles are equal). So by SAS (Side - Angle - Side) criterion.

Step8: Write congruency statement for problem 5

\(\triangle GIL\cong\triangle HKL\)

Step9: Identify congruent parts for problem 6

In \(\triangle WXZ\) and \(\triangle YXZ\), \(WZ = YZ\) (given by marks), \(\angle WZX=\angle YZX = 90^{\circ}\), \(XZ = XZ\) (common side). So by SAS (Side - Angle - Side) criterion.

Step10: Write congruency statement for problem 6

\(\triangle WXZ\cong\triangle YXZ\)

Answer:

1. SAS, \(\triangle BED\cong\triangle AEC\)
2. SAS, \(\triangle VST\cong\triangle UST\)
3. SSS, \(\triangle MNQ\cong\triangle PNQ\)
4. SAS, \(\triangle GIL\cong\triangle HKL\)
5. SAS, \(\triangle WXZ\cong\triangle YXZ\)