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Geometry - Triangles

Multiple Choice Questions

21.

The midpoints of AB and AC of triangle ABC are X and Y respectively. If BC + XY = 12 units, then BC - XY is

10 units
8 units
6 units
6 units

433 Views

22.

In an isosceles $increment ABC comma space$ AD is the median to the unequal side meeting BC at D. DP is the angle bisector of $angle ADB$ and PQ is drawn parallel to BC meeting AC at Q. Then the measure of $angle PDQ$ is

$130 degree$
$90 degree$
$180 degree$
$180 degree$

396 Views

23.

If in △ ABC, DE ∥ BC, AB = 7.5 cm, BD = 6 cm and DE = 2 cm then the length of BC in cm is

269 Views

24.

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG : GF is

1: 2
2 : 1
1 : 3
1 : 3

232 Views

25.
In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is

80°

40°

90°

90°

90°

AC = BC
$angle ABC space equals space angle BAC space equals space 50 degree$
$therefore space space angle ACB space equals space 180 degree space minus space 100 degree space equals space 80 degree therefore space space angle ACD space equals space 180 degree space minus space 80 degree space equals space 100 space space angle CAD space equals space angle CDA space equals space fraction numerator 80 degree over denominator 2 end fraction space equals space 40 degree$

$therefore space space space angle BAD space equals space angle BAC space plus space angle CAD space space space space space space space equals space 50 degree space plus space 40 degree space equals space 90 degree$

675 Views

26.

ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is

70°
110°
80°
80°

906 Views

27.

ΔABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is