Triangles

A triangle ABC is inscribed in a circle where AB is the diameter of the circle. If BC is equal to the radius of the circ...

Which of the following are the angles of a scalene triangle?...

In the following sets, which set represents the sides of a right-angled triangle?...

Points P and S lie on the same side of line segment QR such that ∠PQR = 90°, ∠SRQ = 90°, and PQ = SR. Determine which co...

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles are congruent by SAS criterion if which of the followin...

In a triangle PQR, S is a point on the side QR such that PS is perpendicular to QR. Which of the following options is tr...

By applying which of the following criteria can two triangles NOT be proved congruent?...

In triangle PQR, the bisectors of angles Q and R meet at point O inside the triangle. If the measure of angle QOR is 107...

Two triangles EFG and HIJ are congruent. If the area of ΔEFG is 124 cm², then what is the area of ΔHIJ?...

The angles of a triangle are such that one angle is the average of the other two. What are the angles of the triangle? ...

A right-angled isosceles triangle has an area of 50 square units. Find its hypotenuse (in units)....

In a triangle $PQR$, $S$ is a point on the side $QR$ such that $PS$ is perpendicular to $QR$. Which of the following rel...

The side BC of triangle ABC is produced to a point D. If AC = BC and ∠BAC = 70°, then find the value of 2.5∠ACD − 1.5∠AB...

In triangle ABC, DE is parallel to BC and 5 times AE equals 3 times EC. If AB = 6.4 units, find the length of DB in unit...

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle will be:...

In a triangle PQR, ∠P + ∠Q = 84°. Find the value of ∠R....

In triangle XYZ, A is a point on YZ such that XA = YA. If ∠XYA = 50° and ∠AXZ = 19°, what is the degree measure of ∠XAZ?...

If the medians of a triangle are equal, then the triangle will be:...

In triangle ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, find the length of A...

In triangle LMN, angle L = 118° and side LM = LN. Find the measure of angle N....

Consider a triangle PQR, right angled at R, in which PQ = 29 units, QR = 21 units and ∠PQR = θ. Find the value of cos²θ ...

△ABC is a right-angled triangle with ∠ABC = 90°. If the length of AB is 28 cm and the length of BC is 96 cm, find the ar...

If the angles of a triangle are in the ratio 7 : 8 : 3, then what is the value of the largest angle?...

For triangles, which of the following statement(s) are true? (a) Sum of interior angles is 180°. (b) All interior an...

In a triangle ABC, if (1/2)∠A + ∠B + ∠C = 120º, find the value of (1/4)∠A....

ΔABC and ΔDEF are two triangles such that ΔABC ≅ ΔFDE. If AB = 17 cm, ∠B = 52°, and ∠A = 95°, then which of the followin...

In triangle PQR, S and T are the midpoints of sides PQ and PR, respectively. The length of side QR is 12 cm. If ST is pa...

In triangle ABC, D is the mid-point of BC. If DL is perpendicular to AB and DM is perpendicular to AC such that DL = DM,...

The side BC of triangle ABC is produced to a point D. If AC = BC and angle BAC = 70°, then find the value of angle ACD m...

If the lengths of two sides of an isosceles triangle are 6 cm and 12 cm, then find the length of the third side....

What is the difference in area (in cm²) of ΔABC having sides of 10 cm, 20 cm and 20 cm, and a right angled triangle ΔPQR...

In triangle DEF, DE = 12 cm, EF = 15 cm, and angle DEF = 90°. Triangle DEF is congruent to triangle XYZ. If YZ = 15 cm, ...

Triangles ABC and PQR are congruent with AB = PQ = 8, BC = QR = 10, and angle B = 35°. Find the value of angle P + angle...

Triangle XYZ is an isosceles triangle with sides XY = XZ. If the measure of angle Y is 80°, what is the measure of angle...

In triangles ABD and FEC, ∠BAD = 60°, BD = EC, ∠ABD = ∠FEC = 90°, and AB = FE. Find the ratio of ∠BAD to ∠FCE. ![image....

The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is described with a radius equa...

ΔEFG and ΔHIJ are similar. Also, ∠E = ∠H and ∠F = ∠I. If 3EF = HI and FG = 9 cm, then what is the length of IJ?...

In triangle PQR, M, N, and S are the mid-points of sides PQ, PR, and QR, respectively. If the area of triangle PQR is 46...

In ΔPQR, if 4∠P = 5∠Q = 20∠R, then the value of ∠Q is:...

If each side of an equilateral triangle is 37√3 cm, then what is its altitude (in cm)?...

In triangle PQR, if PT is the median, then which of the following is correct?...

P, Q and R are the three angles of a triangle. If P − Q = 20° and Q − R = 26°, then ∠P is equal to:...

In a triangle PQR, PQ = PR and PT is perpendicular to QR. If PQ = 17 cm and PT = 15 cm, then what is the length of QR in...

Find the area (in cm²) of an equilateral triangle whose sides are 18 cm....

If ∆ABC and ∆QPR are congruent triangles such that AB = 7 cm, AC = 8 cm, ∠B = 65°, and ∠C = 75°, then which of the follo...

In the following sets, which set represents the angles of a triangle?...

The perimeters of two similar triangles ΔRST and ΔABC are 26 cm and 39 cm, respectively. If AB = 24 cm, then what is the...

If ΔPQR ≅ ΔABC, AB = 6 cm, ∠B = 50° and ∠A = 70°, then which of the following is true?...

A pole 10 m long rests slantly against a vertical wall AB making an angle 30° with the horizontal (ground). Find how far...

If the ratio of the areas of two similar triangles is 25 : 144, find the ratio of their corresponding sides....