Mathematics · Quantitative Aptitude

Geometry of Triangles and Angles

846 Questions

Triangle and angle geometry covers angle sums, properties of equilateral shapes, and right triangles. These principles form the basis of advanced quantitative aptitude sections. Practicing spatial problems helps secure points in exams.

Triangle angle sumsPythagorean theoremProperties of equilateral trianglesComplementary and supplementary anglesRight triangle formulas

Geometry of Triangles and Angles Questions

Multiple choice

ABC is a right triangle in which angle B = 90°. The biggest circle possible is inscribed in the triangle. If AB = 8 cm and BC = 6 m, find the radius r of the incircle.

  1. 4 cm

  2. 1 cm

  3. 2 cm

  4. 0.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of right $\triangle$ABC = 1/2 x AB x BC= 1/2 x (6 x 8)cm2 = 24 cm2     AC2 = AB2 + BC2                             64 cm2 + 36 cm2 = 100 cm2. AC = 10 cm.  Also, area ($\triangle$ABC) = ar ($\triangle$OBC) + ar ($\triangle$OCA) + ar ($\triangle$OAB)= 1/2 (BC x r) + 1/2 (AC x r) + 1/2 (AB x r)= 1/2 r (6 + 10 +8) cm = 12 r cm 12 r cm = 24 cm2 $\Rightarrow$ r = 2 cm

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is 

  1. 6.54 cm

  2. 8 cm

  3. 4 cm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Perimeter of triangle is $2{s}=28\ cm\implies s=14$

Inradius of triangle $r=4\implies \Delta=r.s=56$
Volume of prism $=366$ cc
$\implies $ Area of triangle $\times $ height $=366$
Height $=\dfrac{366}{56}=6.54$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

In any triangle, the side opposite to the larger (greater) angle is longer

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A greater angle of a angle is opposite a greater side$.$ Let $ABC$ be a triangle in which angle $ABC$ is greater than angle $BCA;$ then side $AC$ is also greater than side $AB.$ For if it is no greater$,$ then $AC$ is either equal to $AB$ or less$.$

Hence$,$ option $(A)$ is always true$.$

Multiple choice maths triangle inequality construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle

The sides of a triangle (in cm) are given below: 

In which case, the construction of $\triangle $ is not possible?

  1. 8, 7, 3

  2. 8, 6, 4

  3. 8, 4, 4

  4. 7, 6, 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle can be formed if the sum of any two sides of triangle is greater then the third side

In option $C$ , sum of two sides is equal to third side.
So triangle can not be formed.
Option $C$ is correct.