Advertisements
Advertisements
Question
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
Options
PQ < TP
PQ < TQ
TQ < TP < PQ
PQ < TP < TQ
Advertisements
Solution
PQ < TQ
Explanation:
∠Q = 180° – (95° + 65°)
∠Q = 20°
∴ ∠Q < ∠T < ∠P
∴ PT < PQ < TQ
APPEARS IN
RELATED QUESTIONS
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
If ΔABC ≅ ΔABC is isosceles with
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
Which of the following is not a criterion for congruence of triangles?
In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

By ______ test
ΔXYZ ≅ ΔLMN
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.

In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.

In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.

In the following figure, OA = OC and AB = BC.
Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.

In the figure, BC = CE and ∠1 = ∠2. Prove that ΔGCB ≅ ΔDCE.
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
Which of the following rule is not sufficient to verify the congruency of two triangles
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
Two figures are congruent, if they have the same shape.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆YZX ≅ ∆PQR
