SSS Criteria for Congruency

Q. Why is AAA not a property for a congruent triangle?

Q.

The contrapositive of ‘If two triangles are identical’, then these are similar is

1. If two triangles are not similar, then these are not identical

2. If two triangles are not, then these are not similar

3. If two triangles are not identical, then these are similar

4. If two triangles are not similar, then these are identical

Q. If two angles in one triangle are congruent to two angles of a second triangle, and also if the included sides are congruent, then the triangles are ___ .

1. congruent
2. not congruent
3. not similar
4. not equal

Q.

Fill in the Blank.

If in two triangles $PQRandDEF,$ $\mathrm{PR}=\mathrm{EF},\mathrm{QR}=\mathrm{DE},\mathrm{PQ}=\mathrm{FD},$, then $∆\mathrm{PQR}\cong$___.

Q.

In a squared sheet, draw two triangles of equal areas such that

(i) The triangles are congruent.

(ii) The triangles are not congruent.

What can you say about their perimeters?

Q. Question 6
Complete the congruence statements:

$\Delta BCA\cong$ ? $\Delta QRS\cong$ ?

Q.

If lengths of all the sides of two triangles are same, then the triangles are congruent.

1. True

2. False

Q. In triangles ABC and PQR, ∠C = ∠R, BC = QR and ∠B = ∠Q, then by which congruency criteria are these two triangles congruent?

1. A.A.A. criterion
2. S.S.S. criterion
3. S.A.S. criterion
4. A.S.A. criterion

Q.

Question 143

In the following pairs of triangles in below figures, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Q.

If two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle, then the triangles are congruent by ____.

1. SAS congruence condition

2. SSS congruence condition

3. ASA congruence condition

4. RHS congruence condition

Q.

(a) If all the sides of a triangle are equal to the sides of another triangle, will both the triangles be congruent to each other?

(b) If AB is parallel to CD then $△$ABO should be congruent to $△$CDO always. Is this right? [2 MARKS]

Q. In Figure, , the sides BC, CA and BA of a $\Delta ABC$ have been produced to D, E and F respectively. If


$\angle ACD={105}^{\circ }and\angle EAF={45}^{\circ };$ find all the angles of the $\Delta ABC..$

Q.

Question 46

By which congruency criterion, the two triangles in the given figure are congruent?

a) RHS
b) ASA
c) SSS
d) SAS

Q.

Question 48

If $\Delta PQR$ is congruent to $\Delta STU$ as shown in the given figure, then what is the length of TU?

a) 5 cm
b) 6 cm
c) 7 cm
d) Cannot be determined

Q.

In the given figure, if AB = DC and BC = AD, then by which postulate is $△ABC\cong △CDA$ ?

1. SSS

2. ASA

3. RHS

4. SAS

Q.

Consider the figure below:

The two triangles are congruent by SAS criterion only.

1. True

2. False

Q.

Using the information given in the figure, find the values of x and y.

1. $x=56°,y={76}^{\circ }$

2. $x={48}^{\circ },y={56}^{\circ }$

3. $x={48}^{\circ },y={76}^{\circ }$

4. $x={76}^{\circ },y={56}^{\circ }$

Q.

For drawing a triangle LMN exactly same as triangle ABC, which of the following minimum conditions are required? (Given M = ${90}^{\circ }$)

1. MN and LN

2. LM, MN and LN

3. LM, MN, LN and MLN

4. LM, MN, LN, MLN and MNL

Q. Lengths of two pages from the same new notebook are _____ congruent.

1. Never
2. Always
3. May or may not be
4. Data inadequate

Q.

Question 7 (ii)
In a squared sheet, draw two triangles of equal area such that:
The triangles are not congruent.
What can you say about their perimeters?

Q.

If $\Delta ABC\cong \Delta PQR$ , then AB is equal to

1. PR

2. QR

3. PQ

4. Both PR and QR

Q.

Question 73

State whether the statement is True or False.

In $\Delta ABC$, AB = 3.5 cm, AC = 5 cm, BC = 6 cm and in $\Delta PQR$, PR = 3.5 cm, PQ = 5 cm, RQ = 6 cm. Then, $\Delta ABC\cong \Delta PQR$

Q.

In the figure, $△ABCand△BADhaveacommanbaseAB.Given,AC=BDandBC=ADthenfromthefollowingstatements,whicharetrueandwhicharefalse?$

1. $△ABC\cong △BAD$

2. $△BPA\cong △CPB$

3. $△APB\cong △ADP$

4. $△APD\cong △CPB$

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : If ΔXYZ ≅ ΔBAC such that XY = 9 cm, YZ = 7 cm and XZ = 6 cm, then AC equals 7 cm.

यदि ΔXYZ ≅ ΔBAC जबकि XY = 9 cm, YZ = 7 cm तथा XZ = 6 cm, तब AC का मान 7 cm है।

R : Corresponding sides of congruent triangles are equal.

सर्वांगसम त्रिभुजों की संगत भुजाएँ बराबर होती हैं।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q.

Consider the figure below:

The triangles ABC and RPQ are congruent. True/False?

1. True

2. False

Q. In triangles ABC and PQR, ∠C = ∠R, BC = QR and ∠B = ∠Q, then by which congruency criteria are these two triangles congruent?

1. A.S.A. criterion
2. S.A.S. criterion
3. A.A.A. criterion
4. S.S.S. criterion

Q. In the adjoining figure, ABC is a triangle in which AD is the bisector of ∠A. If AD ⊥ BC, show that ∆ABC is isosceles.

Q.

Rahul found 3 pairs of wooden ice-cream sticks in which the sticks in each pair are of the same length as shown below.

Rahul took one stick each from each pair and made a triangle. Likewise, his friend Arjun made another triangle which looked exactly same with the remaining sticks. They realized both these triangles have the same perimeter and are congruent under the ___________ criterion of congruence.

1. SAS

2. SSA

3. SSS

4. ASA

Q.

In the given figure, AB = CF, EF = BD and $\angle$AFE = $\angle$DBC. Then $△$AFE is congruent to $△$CBD by which criterion?

1. SAS

2. SSS

3. ASA

4. None of these

Q.

In the given figure, if AB = AD and CB = CD, then which of the following is true ?

1. $△ABC\cong △ADC$ by SAS postulate

2. $△ABC\cong △ADC$ by SSS postulate

3. If $\angle ABC=x^{\circ }$, then $\angle ADC=x^{\circ }$

4. If $\angle BAC=y^{\circ },$ then $\angle DCA=y^{\circ }$