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

### Question 1

Criteria for congruence of triangles are _________ .

SSS, SAS, ASA, AAS, RHS

SSS, SAS, ASS, AAS, RHS

SSS, SAS, ASA, SSA, RHS

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 _____ .

OD = 12 OC

OD = OC

OD > OC

OD < OC

#### SOLUTION

Solution :B

Consider ΔBOC and ΔAOD

1) AD = BC ( Given )

2) ∠CBO=∠DAO= 90°

3) ∠BOC=∠AOD ......(vertically opposite angles)

∴ΔBOC≅ΔAOD ....[AAS Criterion]⇒ OC = OD ....(congruent parts of congruent triangle)

### Question 3

Consider the figure below:

If ΔBOC≅ΔAOD , and ∠ DOA=30o, then what is the measure of ∠BCO (in degrees) ?

#### SOLUTION

Solution :Since, ΔBOC≅ΔAOD, then ∠BOC=30o. From angle sum property of triangle in ΔBOC, the measure of ∠BCO is 60o.

Since, ΔBOC≅ΔAOD,

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.

True

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.

True

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 ___________ .

x = 15, y = 9

x = 9, y = 15

x = 14, y = 9

x = 15, y = 10

#### SOLUTION

Solution :A

Given, AB=AC

⟹94=6x+4⟹6x=90⟹x=15

In △ABD and △ACD,

(i) ∠ADB=∠ADC=90∘ ... (given)

(ii) AB = AC ... (given)

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

⇒△ABD≅△ADC ... (RHS congruence rule)

Then, BD=CD ... (CPCT)

⇒2y–7=11⇒2y=18⇒y=9

### Question 7

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

△ABD≅△ADC by RHS postulate

△ABD≅△ADC by ASA postulate

BD = DC

If ∠ABD=60∘,then∠ACD=30°

#### SOLUTION

Solution :A and C

In △ABD and △ADC

(i) ∠ADB=∠ADC=90∘ .......(given)

(ii) AD = AD ....... (common)

(iii) AB = AC ....... (given)

(iv) △ABD≅△ADC....... (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?

△ABO≅△CBO by RHS postulate

△ABO≅△CBO by ASA postulate

OA = OC

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)

⇒△ABO≅△CBO ........ (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 ___________.

x=56°,y=76∘

x=48∘,y=56∘

x=48∘,y=76∘

x=76∘,y=56∘

#### SOLUTION

Solution :B

Consider △ABC and △ADC

(i) AB = CD ...... (given)

(ii) BC = DA ...... (given)

(iii) AC = AC ...... (common)∴△ABC≅△CDA ... (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 ?

△ADB≅△ADC by RHS postulate

△ADB≅△ADC by SSS postulate

AB bisects ∠BAC

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)△ABD≅△ACD ......(SSS Postulate)

(v) ∠BAD=∠CAD .....(cpct)

∴ AD bisects ∠ BAC

(vi) ∠ABD=∠ACD .....(cpct)

If ∠BAC=80∘, then ∠ABD=∠ACD=50∘ ( not 80∘)