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Practice each question, then open the answer or worked solution.
Which of the following is not a criterion for congruence of triangles?
(C) SSA
Explanation:
We know that,
Two triangles are congruent, if the side(S) and angles (A) of one triangle is equal to another.
And criterion for congruence of triangle are SAS, ASA, SSS, and RHS.
SSA is not the criterion for congruency of a triangle.
Hence, option C is the correct answer.
If AB = QR, BC = PR and CA = PQ, then
(A) Δ ABC ≅ ΔPQR
(B) ΔCBA ≅ ΔPRQ
(C) ΔBAC ≅ Δ RPQ
(D) Δ PQR ≅ Δ BCA
(B) ΔCBA ≅ ΔPRQ
Explanation:
According to the question,
AB = QR, BC = PR and CA = PQ
Since, AB = QR, BC = PR and CA = PQ
We can say that,
A corresponds to Q, B corresponds to R, C corresponds to P.
Hence, (B) ΔCBA ≅ ΔPRQ
Hence, option B is the correct answer.
In Δ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to
(A) 40° (B) 50° (C) 80° (D) 130°
(B) 50°
Explanation:
According to the question,
Δ ABC, AB = AC and ∠B = 50°.
Since, AB = AC
Δ ABC is an isosceles triangle.
Hence, ∠B = ∠C
∠B = 50° (given)
⇒ ∠C = 50°
Hence, option B is the correct option.
In Δ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to
(A) 80° (B) 40° (C) 50° (D) 100°
(C) 50°
Explanation:
Given: Δ ABC, BC = AB and ∠B = 80°
Since, BC = AB
Δ ABC is an isosceles triangle.
Let, ∠C = ∠A = x
∠B = 80° (given)
We know that,
Using angle sum property,
Sum of interior angles of a triangle should be = 180o
∠A + ∠B + ∠C = 180°
⇒ x + 80° + x = 180°
⇒ 2x = 180° – 80°
⇒ 2x = 100°
⇒ x = 50°
Therefore, ∠C = ∠A = 50°
Hence, option C is the correct answer.
In Δ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is
(A) 4 cm (B) 5 cm (C) 2 cm (D) 2.5 cm
Given: ΔPQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm
Since, ∠R = ∠P
Δ PQR is an isosceles triangle.
Hence, PQ = QR
⇒ PQ = 4cm
Hence, option A is the correct answer.