Free Congruence of Triangles 03 Practice Test - 7th grade 

Question 1

Criteria for congruence of triangles are _________ .

A.

SSS, SAS, ASA, AAS, RHS

B.

SSS, SAS, ASS, AAS, RHS

C.

SSS, SAS, ASA, SSA, RHS

D.

SSS, SAS, ASA, AAS, AAA

SOLUTION

Solution : A

Criteria for congruence of triangles are SSS, SAS, ASA, AAS, RHS.

SSS- Two  triangles are congruent if all the 3 corresponding sides of the given triangles are equal. 

SAS- Two triangles are congruent if 2 corresponding sides of the given triangles and the corresponding angle between those sides are equal to each other. 

ASA- Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding angles and sides of other triangles. 

AAS- Two triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal.

RHS- If the hypotenuse and a side of a right angled triangle are congruent with the hypotenuse and the corresponding side
of the other right angled triangle, then the two triangles are congruent with each other.

Question 2

In the figure given below, AD and BC are equal and perpendicular to the same line segment AB. CD cuts AB at O. Then the relation between OC and OD is _____ .

A.

OD = 12 OC

B.

OD = OC

C.

OD > OC

D.

OD < OC

SOLUTION

Solution : B

Consider ΔBOC  and ΔAOD
1) AD = BC  ( Given ) 
2) CBO=DAO= 90°
3) BOC=AOD ......(vertically opposite angles)


ΔBOCΔAOD ....[AAS Criterion]

OC = OD ....(congruent parts of congruent triangle)

Question 3

Consider the figure below:

If ΔBOCΔAOD , and DOA=30o, then what is the measure of BCO (in degrees) ?


___

SOLUTION

Solution :

Since, ΔBOCΔAOD, then BOC=30o. From angle sum property of triangle in ΔBOC, the measure of BCO is 60o.

Since, ΔBOCΔAOD,

Corresponding angles of the triangles are equal. It gives,
BOC=30o 
BOC+BCO+OBC=180o [Angle sum property]  
BCO​​​​​​​ = 180 - (90 + 30) = 180 - 120 = 60o

Question 4

In two triangles; if a pair of corresponding angles and a side are equal, then the triangles are necessarily congruent.

A.

True

B.

False

SOLUTION

Solution : A

In two triangles,

If a pair of corresponding angles and the included side are equal, then they are congruent [ASA congruence criterion].

If a pair of corresponding angles and a non-included side are equal, then they are congruent [AAS congruence criterion].

Therefore, given statement is true.

Question 5

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

A.

True

B.

False

SOLUTION

Solution : A

If all the side lengths of one triangle are equal to the side lengths of another triangle, then the triangles are congruent. This is called SSS criterion.

Question 6

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

A.

x = 15, y = 9 

B.

x = 9, y = 15

C.

x = 14, y = 9

D.

x = 15, y = 10

SOLUTION

Solution : A

Given, AB=AC
94=6x+46x=90x=15
 

In ABD and ACD,
(i) ADB=ADC=90 ... (given)
(ii) AB = AC ... (given)
(iii) AD = AD ... (common side)
ABDADC ... (RHS congruence rule)
Then, BD=CD ... (CPCT)
2y7=112y=18y=9

Question 7

In the given figure, if AB = AC and ADB=ADC=90, then which of the following is true?

A.

ABDADC by RHS postulate

B.

ABDADC by ASA postulate

C.

BD = DC

D.

If ABD=60,thenACD=30°

SOLUTION

Solution : A and C

In ABD and ADC

(i) ADB=ADC=90 .......(given)

(ii) AD = AD ....... (common)

(iii) AB = AC ....... (given)

(iv) ABDADC....... (RHS Postulate)

(v) BD = DC …… (cpct)

(vi) ABD = ACD=60 .......(cpct)

Hence (A) and (C)

Question 8

In the given figure, if AB = BC and BAO=BCO=90, then which of the following is true?

A.

ABOCBO by RHS postulate

B.

ABOCBO by ASA postulate

C.

OA = OC       

D.

If ABO=60 then, CBO=60

SOLUTION

Solution : A, C, and D


In ABO and CBO

(i) BAO=CAO=90 ........ (given)

(ii) BO = BO .........(common side)

(iii) AB = BC........ (given)

ABOCBO    ........ (RHS Postulate)
 OA = OC.......(cpct)
ABO=CBO=60 ........(cpct)

 

Question 9

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

A.

x=56°,y=76

B.

x=48,y=56

C.

x=48,y=76

D.

x=76,y=56

SOLUTION

Solution : B

Consider ABC and ADC



(i) AB = CD ...... (given)
(ii) BC = DA ...... (given)
(iii) AC = AC ...... (common)

ABCCDA ... (SSS Postulate)

ABC=CDA ..... (CPCT)

x=48

 BCA=DAC ......(CPCT)

y=56

Question 10

In the given figure, if AB = AC and D is the midpoint of BC, then which of the following is true ?

A.

ADBADC by RHS postulate

B.

ADBADC by SSS postulate

C.

AB bisects BAC

D.

If BAC=80, then ABD=80

SOLUTION

Solution : B

In ABD and ACD

(i) AB = AC .........(given)

(ii) BD = CD .........(given)

(iii) AD = AD ..........(common)

(iv)ABDACD ......(SSS Postulate)

(v) BAD=CAD .....(cpct)

AD bisects BAC

(vi) ABD=ACD .....(cpct)

If BAC=80, then ABD=ACD=50 ( not 80)