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In the given figure, AB = PQ, BC = QR and the median AD is equal to the median PM of the other triangle PQR, then ΔABD is congruent ΔPQM by the criterion
- a)AAS
- b)SSS
- c)RHS
- d)SAS
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In the given figure, AB = PQ, BC = QR and the median AD is equal to th...
We are asked to prove that triangle ABD is congruent to triangle PQM.
Step 1: Compare given information
- AB = PQ (given)
- BC = QR (given)
- AD = PM (given, both are medians)
Step 2: Use property of medians
- Since AD is the median of triangle ABC, point D is the midpoint of BC.
So BD = DC = half of BC. - Since PM is the median of triangle PQR, point M is the midpoint of QR.
So QM = MR = half of QR.
Step 3: Use the equality of sides
- From given, BC = QR.
- Therefore, half of BC = half of QR.
- This means BD = QM.
Step 4: Now check corresponding sides of triangles ABD and PQM
- In triangle ABD and triangle PQM:
- AB = PQ (given)
- BD = QM (proved using medians and BC = QR)
- AD = PM (given)
So, all three sides of triangle ABD are equal to the corresponding three sides of triangle PQM.
Step 5: Congruence criterion
- When three sides of one triangle are equal to the three sides of another triangle, the two triangles are congruent by the SSS (Side-Side-Side) criterion.
Final Answer: The correct option is b) SSS.
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