given: line QO congruent to QN, line NM CONGRUENT TO OP Prove: triangle QMP IS ISOCELES
5. TRIANGLE QNM CONGRUENT TO TRIANGLE QOP WHAT IS THE REASON
7. TRIANGLE QMP IS ISOCELES WHAT IS THE REASON
To prove that triangle QMP is isosceles, we need to use the given information and the properties of congruent triangles. Let's break it down step by step:
Step 1: Given that line QO is congruent to line QN.
Reason: Given information.
Step 2: Given that line NM is congruent to line OP.
Reason: Given information.
Step 3: To prove triangle QMP is isosceles, we aim to show that line QM is congruent to line PM.
Step 4: Triangle QNM is congruent to triangle QOP.
Reason: By side-angle-side (SAS) congruence criterion, as we have the following congruent parts:
- Line QN congruent to line OP (given).
- Line NM congruent to line QP (from step 2 and the transitive property of congruence).
Step 5: Since triangle QNM is congruent to triangle QOP, the corresponding sides are congruent, including QM and PM.
Reason: Corresponding parts of congruent triangles are congruent (CPCTC).
Step 6: Therefore, triangle QMP is isosceles since QM is congruent to PM.
Reason: By definition, a triangle is isosceles if it has two congruent sides.
In conclusion, using the given information and the properties of congruent triangles, we have proven that triangle QMP is isosceles.