Congruency of Triangles

Q. In each pair of triangles given below, parts shown by identical marks are congruent. State the test and the one to one correspondence of vertices by which triangles in each pair are congruent and remaining congruent parts.
(1)


(2)

(3)

Q. Which is the angle opposite to the side DE?

1. ∠ E
2. ∠ F
3. ∠ D
4. None of the above

Q. In ∆ ABC , which is the side opposite to ∠ A ?

1. AB
2. None of the above
3. BC
4. AC

Q. Which side is included between ∠ B and ∠ C ?

1. AB
2. AC
3. BC
4. None of the above

Q. If in two triangles ABC and PQR , AB = PQ, AC = QP and BC = QR then

1. ∆ ACB ≅ ∆ PQR
2. ∆ ABC ≅ ∆ PRQ
3. ∆ ACB ≅ ∆ PRQ
4. ∆ ABC ≅ ∆ PQR

Q.

Consider the figure below:

The triangles ABC and PQR are similar.

1. True

2. False

Q.

You went to eat pizza with 3 of your friends. You ordered a small pizza which was equally divided into 4 slices. Prove that all these slices are congruent to each other. [3 MARKS]

Q. Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$
Which congruence criterion do you use to prove $\Delta ABE\cong \Delta CDB$? [3 MARKS]

Q. Which of the following is not a valid congruence criterion for triangles?

1. RHS
2. SSS
3. AAA
4. SAS

Q.

Question 1 (d)
Which congruence criterion do you use in the following?
Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$

Q.

If the adjacent sides of a parallelogram is in the ratio is 2:3 and the perimeter is 50 units, find the sides of the parallelogram

1. If a quadrilateral is a parallelogram, then its diagonal divides it into two congruent triangles

2. If a quadrilateral is a parallelogram, then each pair of opposite sides is equal

3. If a quadrilateral is a parallelogram, then each pair of opposite angles is equal

4. If a quadrilateral is a parallelogram, then its diagonals bisect each other

Q. A central angle measures 105°. Find the measure of its corresponding minor arc and of the major arc corresponding to this minor arc.

Q.

An isosceles triangle ABC has AC = BC. CD bisects AB at D and $\angle CAB={55}^{\circ }$. Then $\angle DCB$ equals

1. ${55}^{\circ }$
2. ${35}^{\circ }$
3. ${70}^{\circ }$
4. ${75}^{\circ }$

Q. What is SAS congruency ?

Q. From the given figure, triangle PQR is congruent to triangle ____.

1. SRP
2. RPS
3. RSP
4. SPR

Q. Which of the following statement is incorrect?

1. The segments of equal lengths are congruent.
2. The angles of equal measures are congruent.
3. The figures which exactly coincide with each other are called congruent figures.
4. ‘congruent’ means not equal in all respects or figures whose shapes and sizes are both the different.

Q.

Let ABC be a triangle such that ∠B = 70° and ∠C = 40°. Suppose D is a point on BC such that AB = AD. Prove that AB > CD.

Q. Triangle ART is congruent to triangle PEN by SSS test. So, AR = PE, RT = EN, and

1. AT = PN
2. AT = PE
3. AT = EN
4. None

Q. Prove that the diagonals of a parallelogram bisect each other.

Q.

Answer the following:

If $∆ABC\cong ∆DEF$, then $AC=$ ?

Q.

For what value of $x$ will $△ABC\cong △XYZ$?

1. 10

Q. "Two triangles ABC and DEF are congruent. "Explain the statement.

Q.

The following figure is a rectangle in which x : y = 4 : 6 , find the values of x and y

1. 72° , 108°

2. 27° , 81°

3. 90° , 90°

4. 36°, 54°

Q.

Triangle ABC is reflected through the mirror XY as shown in the figure. Then which among the given options is congruent to triangle ABC?

1. 

2. 

3. 

4. 

Q. Question 8 (i)
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

Q. If the measure of a central angle is 120°, find the measure of the corresponding minor arc and that of the major arc corresponding to this minor arc.

Q.

Suppose ABC is a isosceles triangle with AB = AC. Side BA is produced to D such that BA = AD. Prove that ∠BCD is a right angle.

Q. The _______ angles of a triangle always add up to ${180}^o.$

1. interior
2. straight
3. exterior
4. outside

Q. The two triangles are congruent by _________ congruency rule.

1. SSS
2. SAS
3. ASA
4. RHS

Q. $\text{If}△ABC\text{and}△PQR$ are to be congruent, name one additional pair of corresponding parts. What criterion did you use?