CONFIDENTIAL 1
Congruence
Grade 4
CONFIDENTIAL 2
Let’s warm up :
Write the name of the polygon which has the following number of sides:
1) 4 sides
2) 5 sides
3) 6 sides
4) 7 sides
CONFIDENTIAL 3
A polygon is a plane shape with straight sides.
Types of Polygons
Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!
Simple Polygon
Complex
Polygon
Let’s review what we did in the last session
We learnt about quadrilaterals.
CONFIDENTIAL 4
Concave or Convex: A convex polygon has no angles pointing inwards. More
precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is concave.
Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is
irregular .
convex Polygon
Concave Polygon
Regular Polygon
Irregular Polygon
CONFIDENTIAL 5
Names of Polygons
Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
CONFIDENTIAL 6
There are many different kinds of quadrilaterals, but all have several things in common: all of them have
four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360
degrees.
But the sides have to be straight, and it has to be 2-dimensional.
A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a
pentagon is a 5-sided polygon, and so on.
Review
CONFIDENTIAL 7
Also opposite sides are parallel and of equal length.
The Rhombus: A rhombus is a four-sided shape where all sides have equal length.
a
cbd
The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e.
90°).
Review
Types of Quadrilaterals
CONFIDENTIAL 8
The Square: A Square is a four-sided shape which has all the sides equal and where every
angle is a right angle (i.e. 90°).
Also opposite sides of a square are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal
length).
Review
CONFIDENTIAL 9
The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are
equal (angles "a" are the same, and angles "b" are the same).
a
b a
b
The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.
NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
A trapezoid is not a parallelogram because only one pair of sides is parallel.
Review
CONFIDENTIAL 10
Let’s start withCongruence
Study these two figures (squares). How are they alike?
If we rotated the pink figure and slid it on top of the yellow one, the two would fit on top of each other
exactly.
All the sides and all the angles are equal, so these two squares are congruent.
The lines crossing the sides (sometimes called "hash marks") are a way to keep track of which side corresponds
to another.
CONFIDENTIAL 11
Two polygons are congruent if they are the same size and shape that is, if their
corresponding angles and sides are equal.
If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called
Congruent:
b°
90°
a°
b°
90°
a°
CONFIDENTIAL 12
is the sign of congruency.
Congruent Angles
Congruent Angles have the same angle in degrees.
135°
135°The angles don't have to point in the same direction.
They don't have to be on similar sized lines.
CONFIDENTIAL 13
Congruence of triangles
If two triangles are congruent, then the sides and angles that match are called corresponding
parts.
A
B C
Let's look at the corresponding parts of triangles ABC and DFE.
D
F
E
A triangle has three sides and three angles.
Angle A corresponds to angle D. Angle B corresponds to angle F. Angle C corresponds to angle E.
CONFIDENTIAL 14
A
B C D
F
E
Side AB corresponds to side DF.
Side BC corresponds to side FE.
Side CA corresponds to side ED.
Congruent figures are named in the order of their corresponding parts. Here, we say "triangle ABC is congruent to triangle DFE," because vertex A corresponds to vertex D, vertex B corresponds to vertex F, and vertex C corresponds
to vertex E.
ABC DFE
CONFIDENTIAL 15
These triangles are congruent. Name the corresponding
parts.
90°
30°
A
B C X
YZ
What is the measure of angle X?
What is the measure of angle Y?
CONFIDENTIAL 16
90°
30°
A
B C X
YZ
Side AB side XY.
Side BC side YZ.
Side CA side ZX.
Angle AB Angle XY.
Angle BC Angle YZ.
Angle CA Angle ZX.
Measure of angle X = 30°
Measure of angle Y = 60°
CONFIDENTIAL 17
BREAK
CONFIDENTIAL 18
Title: Format: WebEx Web BrowserDouble-click to edit
CONFIDENTIAL 19
Assignments
Write whether these figures are congruent.
1) 2)
3) 4)
CONFIDENTIAL 20
These triangles are congruent.
5) What is the measure of angle Z?
120°30°
A B
C
120°
30°
X
Y
Z
4 cm
4 cm
7 cm
6) What is the measure of side XY?
7) What is the measure of side YZ?
8) What is the measure of side ZX?
CONFIDENTIAL 21
These rhombus are congruent. Name the corresponding parts of the following.
A B
CD WX
Y Z
9) side AD
10)side XY
11)Angle A
12)Angle Y
CONFIDENTIAL 22
Two polygons are congruent if they are the same size and shape that is, if their
corresponding angles and sides are equal.
If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called
Congruent:
b°
90°
a°
b°
90°
a°
Very Good!Let's Review
We will learn about Congruency today.
CONFIDENTIAL 23
Congruent Angles
Congruent Angles have the same angle in degrees.
135°135°
The angles don't have to point in the same direction.
They don't have to be on similar sized lines.
Review
CONFIDENTIAL 24
Congruence of triangles
If two triangles are congruent, then the sides and angles that match are called corresponding
parts. A
B C
Let's look at the corresponding parts of triangles ABC and DFE.
D
F
E
A triangle has three sides and three angles.
Angle A corresponds to angle D. Angle B corresponds to angle F. Angle C corresponds to angle E.
Review
CONFIDENTIAL 25
A
B C D
F
E
Side AB corresponds to side DF.
Side BC corresponds to side FE.
Side CA corresponds to side ED.
Congruent figures are named in the order of their corresponding parts. Here, we say "triangle ABC is congruent to triangle DFE," because vertex A corresponds to vertex D, vertex B corresponds to vertex F, and vertex C corresponds
to vertex E.
ABC DFE
Review
CONFIDENTIAL 26
These triangles are congruent. Name the corresponding
parts.
90°
30°
A
B C X
YZ
What is the measure of angle X?
What is the measure of angle Y?
Review
CONFIDENTIAL 27
90°
30°
A
B C X
YZ
Side AB side XY.
Side BC side YZ.
Side CA side ZX.
Angle AB Angle XY.
Angle BC Angle YZ.
Angle CA Angle ZX.
Measure of angle X = 30°
Measure of angle Y = 60°
Review
CONFIDENTIAL 28
You have done a nice job.See you in the next session.