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 maths construction of angles identifying angles acute and obtuse angles types of angle

An angle which measures more than $\displaystyle 0^{o}$ and less than $\displaystyle 90^{o}$ is called:

  1. obtuse

  2. acute

  3. right

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.

An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.
Hence, the answer is acute.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

 $\displaystyle 89^{o}$ is an example of:

  1. obtuse angle

  2. acute angle

  3. right angle

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
An angle with measure $=90^{o}$ is a right angle
An angle with measure $>90^{o}$ is an obtuse angle
An angle with measure $<90^{o}$ is an acute angle

Here, $89^o$ is less than $90^o$. 

Hence, it is an acute angle.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

$\displaystyle 179^{o}$ is an example of:

  1. obtuse angle

  2. acute angle

  3. right angle

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
An angle with measure $=90^{o}$ is a right angle
An angle with measure $>90^{o}$ is an obtuse angle
An angle with measure $<90^{o}$ is an acute angle

Here, $179^o$ is greater than $90^o$ and less than $180^{o}$. 

Hence, it is an obtuse angle.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

An angle which measures $\displaystyle 180^{o}$ is called:

  1. zero angle

  2. right angle

  3. straight angle

  4. acute angle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

An angle which measure $0^0$ is called zero angle.

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.
An angle which measures $90^o$ is called a right angle.

An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.
An straight line makes the angle of $180^o$.
Hence, the answer is straight angle.

Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

A right-angled triangle is formed by a straight line : $3x-4y=12$ with both the axis. Then length of perpendicular from the origin to the hypotenuse is :

  1. $3.5$
  2. $2.4$
  3. $4.2$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given straight line is $3x-4y=12$
$\Rightarrow\frac{x}{4}-\frac{y}{3} = 1$
this line have x intercept y & y- intercept (-3)
so the evaluation of hypotenuse s the given straight line $3x-4y=12$
so, distance of O(0, 0) form the line $3x-4y=12$ is given by
$=\frac{|3\times0-4\times0-12|}{\sqrt{(3)^2+(-4)^2}}$
$=\frac{12}{5}$
$=2.4$

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

If G is the centroid of $\triangle ABC$ and BC = 3, CA = 4, AB = 5 then BG =

  1. $\dfrac { \sqrt { 73 } }{ 3 } $
  2. $\dfrac { \sqrt { 13 } }{ 3 } $
  3. $\dfrac { \sqrt { 52 } }{ 3 } $
  4. $\dfrac { \sqrt { 26 } }{ 3 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triangle with sides 3, 4, 5 is a right triangle. Using Apollonius theorem or coordinate geometry, the length of the median to side AB (c=5) is m_c = 1/2 * sqrt(2a^2 + 2b^2 - c^2) = 1/2 * sqrt(2*16 + 2*9 - 25) = 1/2 * sqrt(7) = sqrt(7)/2. The centroid G divides the median in a 2:1 ratio, so BG = 2/3 * m_c = 2/3 * sqrt(7)/2 = sqrt(7)/3. However, checking the options, sqrt(52)/3 is 2*sqrt(13)/3. Let's re-verify: median to AB is 1/2 * sqrt(2*16 + 2*9 - 25) = sqrt(7)/2. The distance BG is 2/3 of the median. None match perfectly. Re-evaluating: maybe median to BC? m_a = 1/2 * sqrt(2*16 + 2*25 - 9) = 1/2 * sqrt(32+50-9) = sqrt(73)/2. BG = 2/3 * sqrt(73)/2 = sqrt(73)/3. Option A is sqrt(73)/3. Wait, the question asks for BG, which is the segment from vertex B to centroid G. This is 2/3 of the median from B to AC. Median m_b = 1/2 * sqrt(2*a^2 + 2*c^2 - b^2) = 1/2 * sqrt(2*9 + 2*25 - 16) = 1/2 * sqrt(18+50-16) = 1/2 * sqrt(52) = sqrt(52)/2. BG = 2/3 * sqrt(52)/2 = sqrt(52)/3.

Multiple choice maths properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity
State true or false:

In quadrilateral $ABCD$, its diagonals $AC$ and $BD$ intersect at point $O$, such that
$\displaystyle \dfrac{OC}{OA}=\dfrac{OD}{OB}=\dfrac{1}{3}$, then
$\triangle OAB \sim \triangle OCD$

  1. True

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

In $\triangle$s, $OAB$ and $OCD$
$\dfrac{OC}{OA} = \dfrac{OD}{OB}$ (Given)
$\angle AOB = \angle COD$ (Vertically opposite angles)
Thus, $\triangle OAB \sim \triangle OCD$ (SAS rule)