Find whether the pair of triangles below are congruent or not. If yes, then state the criterion of congruency and prove then congruent.
Answers
Answer:
Two triangles are said to be congruent if they are of the same size and same shape. Two congruent triangles have the same area and perimeter. All the sides and angles of a triangle are equal to the corresponding sides and angles of its congruent triangle. We can prove the congruency of any two triangles by using five different properties, which are - SSS, SAS, AAS, ASA, and RHS.
Answer:
Let us discuss them in detail.
What is Congruence in Triangles?
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent. In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z. Then we can say that Δ PQR ≅ ΔXYZ.
congruence in triangles
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other. When we rotate, reflect, and/ or translate a triangle, its position or appearance seems to be different. In that case, we need to identify the six parts of a triangle and their corresponding parts in the other triangle. Consider Δ ABC and ΔPQR as shown below.
A AB = BC = AC and PQ = QR =PRAB = BC = AC and PQ = QR =PR
B ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R
C AB = PQ, BC = QR and ∠B = ∠QAB = PQ, BC = QR and ∠B = ∠Q
D AB = PR, BC = RT and ∠C = ∠TAB = PR, BC = RT and ∠C = ∠T
Q. 3
Aaron wants to prove Δ ABC ≅ ΔDEF using SAS criterion. He knows AB = DE and AC = DF. What additional piece of information does he need?
A ∠C = ∠F∠C = ∠F
B ∠A = ∠D∠A = ∠D
C ∠B = ∠E∠B = ∠E
D ∠A = ∠B∠A = ∠B
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