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Published on: 06/08/2019
Congruence of Triangles
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Questions + Answers key
Take MCQ Mathematics Test
1.
In the given figures, measures of some parts of triangles are given. By applying RHS congruence rule, state which pairs of triangles are congruent? In case of congruent triangles, write the result in symbolic form.
2.
If ΔDEF ≅ ΔPQR Write the part(s) of ΔPQR that corresponds to ㄥF
3.
If ABC ≅ ΔPQRunder the corresponding ABC ↔️ PQR. Write all the corresponding congruent part of the triangles.
4.
RHS congruence condition is applicable to two
Right-angled triangles
Acute-angled triangles
Equilateral angles
Scalene triangles
5.
Two equilateral triangles are congruent if they have same:
angle
side
altitude
median
6.
Two circles are said to be congruent, if they have the same:
radius
area
centre
none of these
7.
Two angles are congruent if they have:
their opening in the same direction
arms of the same length
the same vertex
the same measure
8.
If \(Δ\)ABC≅\(Δ\) PQR, then any \(\angle\)B correspond to:
\(\angle\)R
\(\angle\)Q
None of these
9.
In SAS congruency
Corresponding sides are equal
Corresponding angles are equal
Two corresponding sides and angle included are equal
None of these
10.
Name of the angle included between the sides DE and EF of ΔDEF:
\(\angle\) EFD
None of these
11.
Which congruence criterion do you use in the following?
Given, ZX = RP, RQ =ZY, ㄥPRQ = ㄥXZY. So, ΔPOR ≅ ΔXYZ
ASA rule
SSS rule
RHS rule
SAS rule
12.
By which of the following criterion, the two triangles cannot be proved congruent?
AAA
SSS
SAS
ASA
13.
Number of elements of a triangle is
6
5
4
3
14.
If the three sides of a triangle are respectively equal to the three sides of another triangle, the two triangles are congruent. This is called the __________congruence of triangles
15.
Two rectangles are congruent, if they have the same ________
16.
If \(\triangle \) PQR ≅ \(\triangle \)BAC, then \(\angle \)R=_____ [\(\angle \)C/\(\angle \)B]
17.
If \(\triangle \) PQR ≅ \(\triangle \)BAC, then \(\overline { RQ } \)=________ [\(\overline { CA } \)/\(\overline { AB } \)]
18.
Two angles are said to be congruent, if they have _____
19.
On the basis of adjacent figures match Column A to Column B (if ΔABC ≅ PQR)
Congruence criterion will be
20.
On the basis of adjacent figures match Column A to Column B (if ΔABC ≅ PQR)
AC equal to
21.
If ΔABC ≅ ΔMNR, then find the value of (2x+3y), where x and y shown in the following figures.
22.
When do we call two squares congruent?
23.
One side of a right triangle is equal to its corresponding side of another right triangle. Are the two triangles always congruent?
24.
Write pair of sides which are equal if ΔABC≅ΔMYZ.
25.
In the given figure, triangles ∆ABC and ΔBCD are right angled at A and D respectively. Prove that ΔABC≌ΔDCB.
Is AB = DC ? give reason.
26.
Two poles of height 9 m and 14m stand upright on a plane ground. If the distance between their tops is 13 m, find the distance between their feets.
1.
(i) In ΔPQR and ΔDEF, ㄥQ = ㄥE = 90°
Hypotenuse PR = Hypotenuse DF = 6 cm
Side PQ ≠ Side DE
[∵ PQ = 3 cm and DE = 25 cm]
Therefore, RHS congruence rule is not satisfies.
Hence, ΔPQR and ΔDEF are not congruent.
2.
If ΔDEF ≅ ΔPQR, then corresponding congruent part(s) of the triangle is ㄥF ↔️ ㄥR
3.
All the corresponding congruent parts of ΔABC and ΔPQR are ㄥA ↔️ ㄥP, ㄥB ↔️ ㄥQ, ㄥC ↔️ ㄥR and \(\bar { AB } \leftrightarrow \bar { PQ } ,\bar { BC } \leftrightarrow \bar { QR } ,\bar { AC } \leftrightarrow \bar { RP } \).
4.
(a)
Right-angled triangles
5.
(b)
side
6.
(a)
radius
7.
(d)
the same measure
8.
(c)
\(\angle\)Q
9.
(c)
Two corresponding sides and angle included are equal
10.
(a)
11.
(d)
SAS rule
12.
(a)
AAA
13.
(a)
6
14.
( )
SSS
15.
( )
length and same breadth
16.
( )
\(\angle \)C
17.
( )
\(\overline { CA } \)
18.
( )
equal measure.
19.
( )
RHS
20.
( )
PR
21.
2x+3y=220°
22.
( )
If side of one square is equal to any side of other square.
23.
( )
No
24.
( )
AB = XY
BC= YZ
CA = ZX.
25.
In ∆ABC and ΔDCB,
AC= DB
\(\angle\) BAC = \(\angle\) CDB = 90°
So by R.H.S. congruency we have
ΔABC ≌ΔDBC
\(\Rightarrow\) by C.P.C T., AB = DC
26.
In the above figure, AB and CD are two poles whose heights are 9 m and 14m respectively.
\(\Rightarrow\) AB = EC = 9m
and BD = 13m
DE = 14 - 9
= 5m
Now in right ΔBDE, by Pythagoras
BD2 = BE2 + DE2
132 = BE2 + 52
\(\Rightarrow\) BE2 = (13)2 - (5)2
= 169-25
BE2 = 144
\(\Rightarrow\) BE = \(\sqrt { 144 } \)
\(\Rightarrow\) BE = 12m.
Hence, distance between their feet = 12 m.
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