Tag: theorems on triangles

Questions Related to theorems on triangles

In. triangle ABC,$\angle A$ + $\angle B$ = 144 and$\angle A$ + $\angle C$ = 124.
Calculate smallest angle of the triangle.

maths theorems on triangles theorem of remote interior angles of a triangle use of properties of parallel lines angle sum property of a triangle

  1. $36^o$

  2. $56^o$

  3. $46^o$

  4. none of these

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Correct Option: A
Explanation:

$\angle A + \angle B = 144$...(I)
$\angle A + \angle C = 124$...(II)
In triangle ABC,
$\angle A  + \angle B + \angle C = 180 $
Add, I and II,
$\angle A + \angle B + \angle A + \angle C = 144+ 124$
$180 + \angle A = 268 $
$\angle A = 268 - 180 $
$\angle A = 88$
Put this value in (I)
$\angle A + \angle B = 144$
$88 + \angle B = 144$
$\angle B = 56$
Put this value in (II)
$\angle A + \angle C = 124$
$88 + \angle C = 124$
$\angle C = 36$

If every side of a triangle is doubled, then the area of the new triangle is 'K' times the area of the old one. The value of K is

maths theorems on triangles theorem of remote interior angles of a triangle use of properties of parallel lines angle sum property of a triangle

  1. 2

  2. 3

  3. $\sqrt 2$

  4. 4

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Correct Option: D
Explanation:
Let the area of the triangle be $x$.

We know that the area of the triangle
$=\dfrac{1}{2}\times Height \times Base$
$x=\dfrac{1}{2}\times Height \times Base$              $........ (1)$

According to the question,
$Kx=\dfrac{1}{2}\times 2 \times Height \times 2 \times Base$
$Kx=4\times x$
$K=4$

Hence, this is the answer.

The ratio of the areas of two similar triangles is equal to the

maths theorems on triangles theorem of remote interior angles of a triangle use of properties of parallel lines angle sum property of a triangle

  1. ratio ofcorresponding medians

  2. ratio ofcorresponding sides

  3. ratio of the squares ofcorresponding sides

  4. none of these

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Correct Option: C
Explanation:

The ratio of the areas of two similar triangles is equal to the square of ratio of their corresponding sides.