Triangles Test ...

In the given triangle ABC, AB = AC and DE bisects ∠BDC. DE is parallel to AB. What is the measure of ∠BED?

PQR is an equilateral triangle. Another triangle QRT is attached to it. What is the measure of QTR, if TQR = 35°?

In the given figure PU = UR and TU = ST. If the length of QR is 44 cm, then what is the length of SQ?

In the given triangle, if ∠PQU = ∠QRT = ∠QPS, then what is the ratio of the lengths UT, TS and US, respectively?

In the isosceles △XYZ, XZ = ZY, what is the approximate length of MY, if MX, MN and MO are 10 cm, 16 cm and 6 cm, respectively?

AB and CD are two parallel lines and AD and CB intersect each other at point O. If the lengths of the sides OB, OC and AB are 2 cm, 3 cm and 4 cm, respectively and perimeter of △OCD is 12 cm, then what is the length of OA?

In the given triangle, AM and CS are perpendicular to BC and AB, respectively. If the lengths of CS and BS are 4 cm and 3 cm, respectively and BM is 2 cm less than BC, then what is the value of AB × BS?

ABCD is a rhombus whose diagonals AC and BD intersect at point E. If AB = 10 cm and diagonal BD = 16 cm, then find the length of diagonal AC.

In a triangle ABC, if angle B = 90° and D is a point on BC such that BD = 2DC then _____.

An electrical pole is placed next to a tree. The height of the tree is 12 m and the shadow cast by it is 16 m. Ratio between PT and TA is 1 : 1. Find the height of the electrical pole and distance between the pole and the tree.

A floodlight is 24 m away from a building which is in triangular shape. The distance between their tops is 26 m. If the floodlight is 28 m above ground level. Find the height of the building.

Sides of which three lengths cannot form a triangle?

Two individuals A and B walk towards the South and East directions, respectively with speeds of 13.2 kmph and 22.4 kmph. After travelling for 2.5 hours B stops and A starts travelling towards B. What is the minimum distance that A would have to travel to meet B?

During a military training, each cadet had to start from A and reach B covering 17 km and then reach E which is 8 km from B. From E, the cadets had to travel to C and then to point D and then finally back to A through point E. The distance from E to C was 4 km and that of E to D was 3 km.

(1) Find the distance from A to E.
(2) Find the total distance covered while moving from A to D via B and C.

In triangle ABC, ∠C and in triangle PQR, ∠R are 90°. If A = P, DQ = 2.5 cm and AD is the perpendicular bisector of QP, then find the length of AB.

The area of triangle MNO is 196 cm², which is similar to another triangle PQR having an area 225 cm². In triangle MNO, DM, which is 14 cm in length, is perpendicular to NO and in triangle PQR, PE is perpendicular to QR. Also E divides QR, which is 30 cm in length, in the ratio 4 : 11. What is the length of PQ?

In the given figure, PQRS is a parallelogram. T is a point on side PS such that the ratio of lengths of PT and TS is 2 : 5. Find the length of RU and QU, respectively if the lines TQ and PR intersects at U.

Find RT in the given figure.

In the given triangle DE || AB, find the value of DE in terms of m, n, p.

In the given figure, PT × TS = QT × TR. PT × SR equal to

In the given figure, ABC is an isosceles triangle right angled at A where AB = AC = x cm and area of triangle ABC right angled at A is x cm². Area of right triangle ADE is cm². Find the length of DE.

For each of the following statements, mention T for true and F for false.

i. Sides of two similar triangles are in the ratio 2 : 1, so the areas of these triangles would be in ratio 6 : 1.
ii. Three sides of a right angled triangle are 20 cm, 99 cm and 102 cm.
iii. In triangle ABC, AB = 3 cm, BC = 4 cm, AC = 5 cm and ∠ACB = 90°.
iv. If two sides of two triangles are proportional, then the third side is also proportional and the triangles are similar.

Match the columns:

	Column I		Column II
A	Find DE (in cm)	i	7.5 cm
B	Area of triangle ABC = 168 cm2. Find the value of X.	ii	4 cm
C	△ABC ～ △DEF Find EF in (cm)	iii	7 cm
D	Find IJ (in cm).	iv	5 cm

In triangle ABC, BD is 1 cm less than the length of AC. Find the lengths of BD and QR.

Which of the following statements is/are correct, according to the given triangle, where XY || PQ?



A.
B. △PQR ～△XYR
C. If PQ = 8 cm, XY = 5cm and QR = 6 cm, then XR = 3.75 cm.
D. 2(∠Q + ∠R) = 360 - (∠Y + ∠P)