If $\triangle\text{ABC}\cong\triangle\text{ACB},$ then $\triangle\text{ABC}$ is isosceles with.
- AAB = AC
- BAB = BC
- CAC = BC
- DNone of these
Question types
Triangles question types
335 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
335
Questions
9
Question groups
5
Question types
01
M.C.Q
258 Q→02Fill In The Blanks[1 Marks ]
5 Q→03True False[1 Marks ]
25 Q→041 Marks Question
8 Q→05Match the Following.
7 Q→062 Marks Questions
13 Q→073 Marks Question
7 Q→084 Marks Questions
4 Q→09Case study (4 Marks)
8 Q→Sample Questions
Triangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\triangle\text{ABC}$ is an isosceles triangle with AB = AC and $\angle\text{B} = 65^\circ,$ find $\angle\text{A}.$
- A70º
- B50º
- C60º
- DNone of these
- A$\triangle\text{ABC}\cong\triangle\text{ABD}$
- B$\angle\text{C}=\angle\text{D}$
- C$\text{All are true}$
- D$\text{BC = BD}$
If $\triangle\text{ABC}≅\triangle\text{LKM},$ then side of $\triangle\text{LKM}$ equal to side AC of $\triangle\text{ABC}$ is:
- ALM
- BKM
- CNone of these
- DLK
If all the three angles of a triangle are equal, then each one of them is equal to:
- A90º
- B45º
- C60º
- D30º
An exterior angle of a triangle is always greater than either of the interior ___________. (Adjacent angles, Opposite angles, Right angles)
An exterior angle of a triangle is equal to the two _______ opposite angles. (Interior, Exterior, Adjacent)
Angles opposite to equal sides of a triangle are _______. (Equal, Different, Supplementary)
A triangle cannot have more than One _______. (Acute angle, Right angle, Obtuse angle)
A triangle cannot have more than obtuse _____ angles. (One, Two, Three)
Angles opposite to equal sides of a triangle are equal.
If any two sides of a right triangle are respectively equal to two sides of other right triangle then the two triangle are congruent.
If the bisector of the verical angle of a triangle bisects the base, then the triangle may be isosceles.
The two alitutde corresponding to two equal sides of a triangle need not be equal.
The measure of each angle of an equilateral triangle 60º.
AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB (See figure)
| Column 1 | Column 2 | ||
| Q.1. | $\triangle X Y Z$ if $\angle Y=90^{\circ}$ and $XY = YZ$ ,then $\angle X=$ | A. | 45° |
| Q.2. | in$\triangle X Y Z$ if $XY = XZ$ and $\angle X=80^{\circ}$,then $\angle Y=$ | B. | 50° |
| C. | 20° |
| Column 1 | Column 2 | ||
| Q.1. | in$\triangle A B C$ and $\triangle P Q R$ ,if $\frac{A B}{P Q}=\frac{B C}{R Q}=\frac{A C}{P R}=1$ ,then $\triangle A B C \cong \triangle$ | A. | ABC |
| Q.2. | in $\triangle A B C$ and $\triangle X Y Z$ if $\angle A=\angle X, \angle C=\angle Z$ and $AB =$ XY ,then $\triangle A B C \cong \triangle$ | B. | PQR |
| C. | XYZ |
| Column 1 | Column 2 | ||
| Q.1. | $\Delta P Q R$ and $\Delta X Y Z$ ,if $\angle P=\angle Z, \angle Q=\angle Y$ and $PQ = YZ$ ,then $\Delta PQR \cong \Delta \ldots \ldots $ | A. | YXZ |
| Q.2. | in$\Delta ABC$ and $\Delta XYZ$ ,if $\angle A =\angle X , \angle C =\angle Z$ and $AB = XY$ ,then $\Delta ABC \cong \Delta \ldots \ldots .$ | B. | ZYX |
| C. | XYZ |
| Column 1 | Column 2 | ||
| Q.1. | if $\Delta P Q R \cong \Delta Y X Z$ , then $\angle \ldots \ldots . .=\angle YZX$. | A. | RQP |
| Q.2. | In $\Delta ABC$ and $\Delta PQR$ ,if $AB = QR , BC = PQ$ and $AC = PR$, then $\Delta ABC \cong \Delta \ldots \ldots .$. | B. | PRQ |
| C. | QRP |
| Column 1 | Column 2 | ||
| Q.1. | In $\Delta ABC$ and $\Delta PQR$ , if $AB = PQ , BC = PR$ ,and $\angle B =\angle P$ , then $\Delta ABC \cong\ldots\ldots$. | A. | $\Delta RPQ$ |
| Q.2. | In $\Delta ABC$ and $\Delta PQR$ ,if$\frac{ AB }{ PR }=\frac{ BC }{ QP }=\frac{ CA }{ RQ }=1$ , then $\Delta ABC \cong\ldots\ldots$ | B. | $\Delta QPR$ |
| C. | $\Delta PQR$ |
ABC is an isosceles triangle with AB = AC. Draw AP $\perp$ BC to show that $\angle$B = $\angle$C.
View full solution →BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that a triangle ABC is isosceles.
ABC is a right-angled triangle in which $\angle $A = ${90^ \circ }$ and AB = AC. Find $\angle $B and $\angle $C.
View full solution →ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that $\triangle \mathrm { ABE } \cong \triangle \mathrm { ACF },$ AB = AC i.e. $\triangle$ABC is an isosceles triangle.
View full solution →Angles opposite to equal sides of an isosceles triangle are equal.This result can be proved in many ways. One of the proofs is given here.
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
View full solution →- AD bisects BC
- AD bisects $\angle$A.
Show that the angles of an equilateral triangle are 60° each.
$\Delta$ ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB(See figure). Show that $\angle$ BCD is a right angle.
View full solution →Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal.
In a toy game, a robot starts from Home, picks an object from the Shop, delivers it to the Client and goes back Home.
8. Which is the longest segment of the path travelled by the robot? Write the correct words.
9. Rita says, ‘For two triangles to be congruent, any three parameters of the six (3 sides and 3 angles) should be equal.’
Give examples in favour of and against her statement.
10. ‘Two triangles with a pair of equal angles are congruent.’
Why is it necessary to have the side between the two angles be of the same length for both the
triangles?
In the given figure, ∆AFB ≅ ∆AFG, ∆ADE ≅ AGE and ∠EAF = 45°.
1. What is the measure of ∠DAB?
A. 60°
B. 90°
C. 120°
D. 135°
2. What is the length of AD?
3. What is the area of the shaded region?
A. 12.5 cm²
B. 15 cm²
C. 20 cm²
D. 36 cm²
Generate a Triangles paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.