Congruence of Triangle
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In the given figure ΔBAC = ΔQRP by SAS criterion of congruence. Find the value of x and y.
Write the rule of congruence in the following pairs of congruent triangles.
In the given figure, ΔQPS = ΔSRQ. Find each value.
(a) x
(b) ∠PQS
(c) ∠PSR
In the given figure, name
(a) the side opposite to vertex A
(b) the vertex opposite A to side AB
(c) the angle opposite to side AC
(d) the angle made by the sides CB and CA
In the given figure, state the rule of congruence followed by congruent triangles LMN and ONM.
Lengths of two sides of an isosceles triangle are 5 cm and 8 cm, find the perimeter of the triangle.
In the given figure, PQ = CB, PA = CR, ∠P = ∠C. Is ΔQPR = ΔBCA? If yes, state the criterion of congruence.
In the given figure, PQ || RS and PQ = RS. Prove that ΔPUQ = ΔSUR.
In the given congruent triangles under ASA, find the value of x and y, ΔPQR = ΔSTU.
In the given figure, PQR is a triangle in which PQ = PR. QM and RN are the medians of the triangle. Prove that
(i) ΔNQR = ΔMRQ
(ii) QM = RN
(iii) ΔPMQ = ΔPNR
In the given figure, state whether ΔABC = ΔEOD or not. If yes, state the criterion of congruence.
In ΔABC, medians BD and CE are equal and intersect each other at O. Prove that ΔABC is an isosceles triangle.
In the given figure, AP = BQ, PR = QS. Show that ΔAPS = ΔBQR
Without drawing the figures of the triangles, write all six pairs of equal measures in each of the following pairs of congruent triangles.
(i) ΔABC = ADEF
(ii) ΔXYZ = ΔMLN
Observe the figure and state the three pairs of equal parts in triangles ABC and DCB.
(i) Is ΔABC = ΔDCB? Why?
(ii) Is AB = DC? Why?
(iii) Is AC = DB? Why?
In the following figure, show that ΔPSQ = ΔPSR.
Prove that the lengths of altitudes drawn to equal sides of an isosceles triangle are also equal.
(i) ∠TRQ = ∠SQR?
(ii) If ∠TRQ = 30°, find the base angles of the ΔPQR.
(iii) Is ΔPQR an equilateral triangle?
Can two equilateral triangles always be congruent? Give reasons.
Examine whether the given triangles are congruent or not.