# Free Congruence of Triangles 03 Practice Test - 7th grade

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.

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)

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

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.

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.

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

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) 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)

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

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) 