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.