Question

use sss to explain why the triangles in each pair are congruent.

1. $\triangle jkmcong\triangle lkm$
2. $\triangle abccong\triangle cda$

use the flowchart to determine, if possible, whether the following pairs of triangles are congruent. if congruent, write asa, aas, or hl - the postulate you used to conclude that they are congruent. if it is not possible to conclude that they are congruent, write no conclusion.
1.
2.
3.
4.

Explanation:

Step1: Analyze the first pair of triangles

For the first pair of triangles (the ones with vertices \(O, P, Q\) and \(S, T, U\)), we only know that one angle is equal (the marked angles). There is not enough information (no side - side - side, side - angle - side, angle - side - angle, etc. congruence criteria met) to prove congruence.

Step2: Analyze the second pair of triangles

For the second pair of triangles (\(\triangle ABC\) and \(\triangle XYZ\)), we have two sides equal (the marked sides) and one non - included angle equal. The SSA (side - side - angle) is not a valid congruence criterion (except for right - angled triangles in the case of HL). So, we cannot conclude congruence.

Step3: Analyze the third pair of triangles

For the third pair of triangles (\(\triangle SUT\) and \(\triangle VWX\)), we only know that one angle is equal (the marked angles). There is not enough information (no side - side - side, side - angle - side, angle - side - angle, etc. congruence criteria met) to prove congruence.

Step4: Analyze the fourth pair of triangles

For the fourth pair of triangles (\(\triangle PQH\) and \(\triangle DEF\)), we have a right - angle (marked right angles), the hypotenuse (the longer side) equal (marked equal) and one leg equal (marked equal). By the HL (Hypotenuse - Leg) congruence criterion for right - angled triangles, \(\triangle PQH\cong\triangle DEF\).

Answer:

1. no conclusion
2. no conclusion
3. no conclusion
4. \(\triangle PQH\cong\triangle DEF\) by HL