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∘)