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LESSON 36
Congruency and Similarity
MPM2D | MCR3U
IB MYP 5 MATHEMATICS EXTENDED
Pearson
IB CONTENTS
11.02 Similar Triangles
11.03 Using Scales Factors to Find Unknown
Sides
Geometry and
Trigonometry
LESSON PLAN
D
ONTARIO EXPECTATIONS
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11.04 Similar Triangle Proofs
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Congruent
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MPM2D
Trigonometry
Prepared by Dr. Benedict Hung
TEXTBOOK
Pearson
Pg. 294 – Pg. 313
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In an isosceles triangle
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the base angles are equal
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the line joining the apex to the midpoint of the base bisects the
vertical angle and meets the base at right angles
Converses of the isosceles triangle theorem
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if a triangle has two equal angles then it is isosceles
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the angle bisector of the apex of an isosceles triangle bisects the
base at right angles
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the perpendicular bisector of the base of an isosceles triangle
passes through its apex
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KEY TERMS
congruency, similarity,
isosceles triangle theorem,
scale factor
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FORMULAE & STATEMENTS
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The symbol for congruency is 
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To say that ABC  DEF means that
AB  DE
A  D
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E
C
F
B  E and BC  EF
D
C  F
AC  DF
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The order that the triangles are listed is important. It lets you know
what angles and sides are equal.
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There are three different conditions for congruent triangles:
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Side-Side-Side Congruence ( SSS  )
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Side-Angle-Side Congruence ( SAS  )
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Angle-Side-Angle Congruence ( ASA  )
The symbol for similarity is ~
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To say that ABC ~ DEF means that B
D
A  D
C
AB BC
AC
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B  E and


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DE EF
DF
C  F
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The order that the triangles are listed is important. It lets you knowF
what angles are equal and what sides are proportional.
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There are three different conditions for congruent triangles:
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Side-Side-Side Similarity ( SSS ~ )
Side-Angle-Side Similarity ( SAS ~ )
Angle-Angle Similarity ( AA ~ )
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AB BC AC
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 n , n is the scale factor.
DE EF DF
the length of any side of ABC  n  (length of the
corresponding side of DEF )
the length of the altitude of ABC  n  (length of the
corresponding altitude of DEF )
perimeter of ABC  n  (perimeter of DEF )
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area of ABC  n 2  (area of DEF )
If ABC ~ DEF , then
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For ABC ~ KLM . AB  8cm and KL  10m . The area of KLM is 40cm2 .
Find the area of ABC .
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10cm
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8cm
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RST ~ PQW . Find the unknown side lengths.
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24cm
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12cm
14cm
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36cm
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ASSIGNMENT
Pearson
Pg. 295 # 2, 5, 6, Pg. 298 # 6 – 8
Pg. 306 # 2 – 4, 6, 7, Pg. 311 # 1, 2, 4, 6, 7bc
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IB MYP 5 Mathematics Extended  MPM2D  MCR3U  Unit 3 – Coordinate Geometry
Prepared by Dr. Benedict Hung
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