Question

4 - 3 additional practice
proving and applying the sas and sss congruence criteria
label each pair of triangles congruent by sas, congruent by sss, or not enough
information.
1.
2.
3.
4.

Explanation:

1. Analyze the first pair of triangles

• In the first pair of triangles, we have two right - angled triangles.
• For right - angled triangles, if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, they are congruent by SAS (since the right angles are equal).

2. Analyze the second pair of triangles

• In the second pair, we have \(AC = CD\), \(BC = CE\), and \(\angle ACB=\angle DCE\) (vertically opposite angles).
• By the SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle DEC\).

3. Analyze the third pair of triangles

• In the third pair, we have two sides equal (\(DF = JL\), \(EF = KL\)) but the included angles are not given to be equal.
• So, there is not enough information to prove congruence.

4. Analyze the fourth pair of triangles

• In the fourth pair, we have \(UT = WX\), \(UV = WV\), \(TV = XV\).
• By the SSS (Side - Side - Side) congruence criterion, \(\triangle TUV\cong\triangle XWV\).

Answer:

1. Congruent by SAS
2. Congruent by SAS
3. Not enough information
4. Congruent by SSS