Congruency of Triangles

Q. Question 7
In $\Delta ABCand\Delta DEF,\angle B=\angle E,\angle F=\angle C$ and AB = 3DE. Then the two triangles are

(A) Congruent but not similar
(B) Similar but not congruent
(C) Neither congruent not similar
(D) Congruent as well as similar

Q. If △ABC is congruent to △PQR and AB = 5 cm, then what is the length of PQ?

1. 3 cm
2. 5 cm
3. 4 cm
4. 6 cm

Q.

Question 134

In each of the given pairs of triangles in given figures, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Q. In the given figure, AD = CD and AB = CB.
(i) State the three pairs of equal parts in ∆ABD and ∆CBD.
(ii) Is ∆ABD ≅ ∆CBD? Why or why not?
(iii) Does BD bisect ∠ABC? Give reasons.

Q. If triangles ABC and EFG are congruent, then the angle of triangle ABC that correspond to angle G is

1. Angle A
2. Angle C
3. Angle B
4. Angle A and Angle B

Q. If $△PQR\cong △XYZ$,
then of $△PQR$ corresponds to side XY of $△XYZ$.

1. side PQ
2. side QR
3. side RP

Q. If triangles PQR and ABC are congruent, then angle Q corresponds to _____.

1. angleA
2. angle B
3. angle C
4. Cannot be determined

Q.

If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the Corresponding congruent parts of the triangles.

Q. Consider the figure given below:

If $△BOC\cong △AOD$ and $\angle DOA={30}^{\circ }$, then what is the measure of $\angle BCO$?

1. 60${}^{\circ }$
2. 30${}^{\circ }$
3. 50${}^{\circ }$
4. 40${}^{\circ }$

Q. Question 5
In the figure, the two triangles are congruent. The corresponding parts are marked. Complete the congruent statement $\Delta RAT\cong$ ?

Q. If, $△$ABC is congruent to $△$DEF as side AB = side DE and side BC = side EF, then, $\angle$C corresponds to which angle of $△$DEF?

1. $\angle$F
2. $\angle$E
3. $\angle$D
4. None of the above

Q.

If $\Delta ABC\cong \Delta RQP$ , then $\angle P$ = _____ .

1. $\angle C$

2. $\angle B$

3. Both $\angle A$ and $\angle B$

4. $\angle A$

Q. Which information is needed to make ABC congruent to PQR in the given figure?

1. QR = AB
2. PR = AB
3. PQ = AC
4. PQ = AB

Q. If triangle XYZ is congruent to triangle RPQ then XY= _______ and angle R =___________

Q.

In $∆ABC,$$AD$the angle bisector of $\angle A$meets side $BC$in $D.$If $\angle ADC={90}^o,$prove that $∆ABC$is an isosceles triangle.

Q.

(a) Show with an example that two triangles can't be congruent using AAA criterion.

(b) Which congruence criterion will you use in the following?

Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

[3 MARKS]

Q. If $△$DEF $\cong$ $△$PQR, then,

1. DE = PQ, EF = QR, FD = RP
2. DE = PQ, EF = RP, FD = QR
3. DE = RP, EF = PQ, FD = QR
4. DE = RP, EF = QR, FD = PQ

Q.

In triangles ABC and PQR, AB = PQ, BC = QR and angle B = angle Q, then they are congruent according to?

1. SAS criteria

2. AAA criteria

3. ASA criteria

4. SSS criteria

Q.

Question 142 (ii)

Without drawing the triangles write all six pairs of equal measures in the given pair of congruent triangles.

$\Delta ABC\cong \Delta LMN$

Q. Two congruent triangles, $△ABC$ and $△QRP$, have $\angle A$ = $\angle Q$ = 40${}^{\circ }$, $\angle R$ = 65${}^{\circ }$ and QR = AB, then $\angle B$ = ____ .

1. 50${}^{\circ }$
2. 75${}^{\circ }$
3. 65${}^{\circ }$
4. 80${}^{\circ }$

Q.

What is the purpose of geometry?

Q. Is SSS, SAS, ASA and AAS criteria the same?

Q.

In triangles ABC and PQR, ∠A = ∠P, AB = PQ and ∠B = ∠Q, then they are congruent according to?

1. SSS criteria

2. SAS criteria

3. AAA criteria

4. ASA criteria

Q.
$△$PST $\cong$ $△$RQT and PS is parallel to RQ. Find the side of $△$RQT that corresponds to side ST of $△$PST.

1. TR
2. QT
3. RQ
4. SR

Q. If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is

1. Isosceles
2. Scalene
3. Equilateral
4. Right-angled

Q. In △ABC and △MNO, ∠A = 80°, ∠B = 30°, AB = 7 cm, ∠M = 80°, MN = 7 cm, ∠O = 30°. By which criteria are the triangles congruent?

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

Q.

The adjoining figure refers to which of the congruency.

1. RHS

2. SAS

3. SSS

4. ASA

Q.

Given that quadrilateral ACBD is a kite. By which congruency property are the triangles ACB and ADB congruent?

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

Q. If two triangles are congruent, then the ____ sides are equal.

1. corresponding
2. adjacent
3. None of the above
4. opposite

Q. Given $△ABC\cong △QRP$
If, $\angle A=\angle Q={60}^{\circ }\text{and}\angle R={40}^{\circ }$, then $\angle C$ measures .

1. 80°
2. 60°
3. 100°