Download Remedial - MoreMaths

1. Congruence of Plane Figures
Description
Congruence of
line segments
Congruence of
angles
Reflect and Review

Teasers
See below the
table.
Two line segments are said to be
congruent if they have the same
length.
A
B
C
D

If ̅̅̅̅ ̅̅̅̅, then ̅̅̅̅ and ̅̅̅̅ have
the same length, and we write it as:
AB = CD.

Two angles are said to be congruent if
1) Draw an angle
they have same measure.
P
A
congruent to
PQR.
Answers
1) ̅̅̅̅
̅̅̅̅̅
P
B

Congruence of
triangles

C
Q
If ABC PQR, then ABC and
PQR have same measure, and we
write it as: mABC = mPQR.
Q
1) Two triangles
∆EFG and ∆LMN
are congruent by
the
correspondence
∆GEF  ∆MNL.
Write the parts
of ∆LMN that
corresponds to
a) E
b) ̅̅̅̅
If two triangles are congruent then
their six elements (three sides and
three angles) of one triangle are
congruent to the six elements of the
other triangle.
A
B
R
X
C
Y
R
1) a) N
b)
Z
1
Consider two triangles, Δ ABC and Δ
XYZ, in which A = X, B = Y and
C = Z, and AB = XY, BC = YZ and AC
= XZ.
Here, we say that the two triangles
are congruent under the
correspondence A X, B Y and
C Z. This can be written as ABC
XYZ.

If any two triangles, ΔABC and ΔPQR
are congruent under the
correspondence ABC QRP, then
A = Q, B = R, C = P, and
̅̅̅̅= ̅̅̅̅, ̅̅̅̅ = ̅̅̅̅ and ̅̅̅̅ = ̅̅̅̅ .
Teasers
1) Find the line segments that are congruent to ̅̅̅̅.
Y
B
X
A
M
D
Q
C
N
P
2. Criteria for Congruence of Triangles
Description
Reflect and Review
SSS Congruence
criterion
If the three sides of one
triangle are equal to the
three corresponding
sides of another triangle,
then the triangles are
congruent.
1) If ABCDE is a regular
pentagon, prove that
∆ACD is isosceles.
A
B
D
A
C
In ∆ABC and ∆ADC,
AB = AD (Property of rhombus)
BC = DC (Property of rhombus)
AC = AC (Common side)
Thus, ∆ABC  ∆ADC (SSS congruence
2
Teasers
E
B
D
C
rule).
1) In the fig, AB = DE, AC =
DF and BAC = EDF.
Prove that
if
F and C are midpoints
of BC and EF
respectively.
SAS Congruence
criterion
If two sides and the angle
included between them
of one triangle are
respectively equal to two
sides and the angle
included between them
of another triangle, then
the two triangles are
congruent.
D
E
B
A
A
C
B
F
In ∆ABC and ∆ADE,
AB = AD (given)
AC = AE (given)
BAC = EAD (vertically opposite
angles)
C
Thus, ∆ABC  ∆ADE (SAS congruence
rule).
ASA Congruence
criterion
D
E
1) In the trapezium ABCD,
if AD = BC, OAB =
OBA and OCD =
ODC then prove that
OA = OB and OC = OD.
W
L
V
If two angles and the
included side of a triangle
N
M
are equal to two
corresponding angles and
In ∆LMN and ∆WVU,
the included side of
another triangle, then the LMN = WVU (given)
LNM = WUV and (given)
triangles are congruent.
MN = VU (given)
U
O
A
Thus, ∆LMN  ∆WVU (ASA
congruence rule).
If the hypotenuse and
one side of a right-angled
triangle are respectively
equal to the hypotenuse
and one side of another
right-angled triangle,
then the right triangles
are congruent.
A
C
B
1) In the quadrilateral
PQRS, PS = QR and
PQS = RSQ = 900.
Prove that PQRS is a
parallelogram.
X
RHS Congruence
criterion
C
D
Y
Z
B
3
In the right angled triangles ACB and
XYZ,
ACB = XYZ
AB = XZ and
AC = XY
Thus, ∆ACB  ∆XYZ (RHS congruence
rule).

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