Mathematics · Quantitative Aptitude

Geometry of Triangles and Angles

758 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 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)

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

In triangle ABC ; M is mid-point of AB, N mid-point of AC and D is any point in base BC. Then:

  1. MN bisects AD

  2. MN divides AD in the ratio 1:3

  3. MN divides AD in the ratio 1:2

  4. MN divides AD in the ratio 1:4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In $\triangle ABC$, $M$ is mid point of $AB$ and $N$ is mid point of $AC$
$D$ is any point of BC
Now, Join AD and MN such that they met at O
In $\triangle ABC$
M is mid point of AB and N is mid point point of AC
Hence, $MN \parallel BC$ and $MN = \frac{1}{2} BC$

Now, In $\triangle ABD$
$MO \parallel BC$ and M is mid point of AB
Thus, $O$ is mid point of AD
Hence, $MN$ bisects $AD$

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

If in two triangles $DEF$ and $PQR$, $\angle D=\angle Q$ and $\angle R=\angle E$, then which of the following is not true?

  1. $\cfrac{EF}{PR}=\cfrac{DF}{PQ}$
  2. $\cfrac{DE}{PQ}=\cfrac{EF}{RP}$
  3. $\cfrac{DE}{QR}=\cfrac{DF}{PQ}$
  4. $\cfrac{EF}{RP}=\cfrac{DE}{QR}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given triangles DEF and PQR, with angle D = angle Q and angle R = angle E. By AA similarity, triangle DEF is similar to triangle QRP. The corresponding sides are proportional: DE/QR = EF/RP = DF/QP. Option B claims DE/PQ = EF/RP, which is not necessarily true because PQ is not the corresponding side to DE.

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

If in the triangles $ABC$ and $DEF$, angle $A$ is equal to angle $E$, both are equal to ${40}^{o}$, $AB:ED=AC:EF$ and angle $F$ is ${65}^{o}$, then angle $B$ is:

  1. ${35}^{o}$
  2. ${65}^{o}$
  3. ${75}^{o}$
  4. ${85}^{o}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given triangle ABC and DEF. Angle A = Angle E = 40 degrees. AB/ED = AC/EF. This satisfies the SAS similarity criterion, so triangle ABC is similar to triangle EDF. Therefore, Angle B = Angle D and Angle C = Angle F. We are given Angle F = 65 degrees, so Angle C = 65 degrees. In triangle ABC, Angle A + Angle B + Angle C = 180. 40 + Angle B + 65 = 180 => Angle B = 180 - 105 = 75 degrees.