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Geometry - Triangles

Multiple Choice Questions

In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 10 cm, 5 cm and 6 cm respectively. What is the length of BC?

9 cm
2 cm
3 cm
11 cm

Δ DEF and Δ GHI are similar triangles. Length of DE is 4 cm and length of the corresponding side GH is 9 cm. What is the ratio of areas of Δ DEF and Δ GHI?

81 : 16
4 : 9
16 : 81
9 : 4

The internal bisectors of the $angle straight B$ and $angle straight C$ of the $increment ABC$ , intersect at O. If $angle straight A space equals space 100 degree$ , then the measure of $angle BOC$ is

$110 degree$
$140 degree$
$120 degree$
$120 degree$

285 Views

Given that, $increment ABC space tilde space space increment PQR.$ If $fraction numerator area left parenthesis increment PQR right parenthesis over denominator area left parenthesis increment ABC right parenthesis end fraction space equals 256 over 441$ and PR = 12 cm, then AC is equal to

15.5 cm
16 cm
$12 square root of 2 cm$
$12 square root of 2 cm$

218 Views

In $increment ABC$ , D and E are two mid-points of sides AB and AC, respectively. If $angle BAC space equals space 40 degree$ and $angle ABC space equals space 65 degree$ then $angle CED$ is

$75 degree$
$130 degree$
$125 degree$
$125 degree$

208 Views

Given an equilateral $increment ABC$ , D, E, F are the mid-points of AB, BC and AC respectively. Then, the quadrilateral BEFD is exactly a

square
rectangle
trapezium
trapezium

200 Views

The heights of two similar right angled triangles and are 48cm and 36 cm. If OP = 12 cm, then LM is

16 cm
20 cm
12 cm
12 cm

217 Views

8.
In the given figures, the lengths of the sides of $increment ABC$ and $increment PQR$ are given and they are given in same units. Also, $angle straight A$ and $angle straight B$ are given. The value of $angle straight P$ is

$36 degree$
$38 degree$
$40 degree$
$40 degree$

40 degree

From the figure,
$AB over RQ space equals fraction numerator 3.8 over denominator 7.6 end fraction space equals space 1 half$
$BC over PQ equals 6 over 12 equals 1 half$
and $AC over RP equals fraction numerator 3 square root of 3 over denominator 6 square root of 3 end fraction equals 1 half$
   $angle straight A space equals space angle straight R space equals space 80 degree angle straight B space equals space angle straight Q space equals space 60 degree$
In $increment ABC comma$
   $angle straight A plus angle straight B plus angle straight C space equals 180 degree$
(angle sum property of a triangle)
$angle straight C space equals space 180 degree minus left parenthesis 80 degree plus 60 degree right parenthesis$
   $equals 180 degree minus 140 degree space equals space 40 degree$
$increment ABC space tilde space increment PQR$
i.e.    $angle straight P space equals space angle straight C space equals space 40 degree$

171 Views

In two similar triangles ABC and MNP, if AB = 2.25 cm, MP = 4.5 cm and PN = 7.5 cm and m $angle ACB$ = m $angle MNP$ and m $angle ABC$ = m $angle MPN$ , then the length of side $BC with bar on top$ , (in cm) is