Congruence Grade 4 CONFIDENTIAL

Write the name of the polygon which has the following number of sides: Let’s warm up : Write the name of the polygon which has the following number of sides: 4 sides 5 sides 6 sides 7 sides CONFIDENTIAL

We learnt about quadrilaterals. Let’s review what we did in the last session We learnt about quadrilaterals. 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 CONFIDENTIAL

If there are any internal angles greater than 180° then it is concave. 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. convex Polygon Concave Polygon Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular . Regular Polygon Irregular Polygon CONFIDENTIAL

Names of Polygons Name Sides Shape Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 CONFIDENTIAL

But the sides have to be straight, and it has to be 2-dimensional. Review 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. But the sides have to be straight, and it has to be 2-dimensional. 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. CONFIDENTIAL

Types of Quadrilaterals Review Types of Quadrilaterals The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e. 90°). 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 c b d CONFIDENTIAL

Also opposite sides of a square are parallel. Review 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). CONFIDENTIAL

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! Review 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 NOTE: Squares, Rectangles and Rhombuses are all Parallelograms! The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel. A trapezoid is not a parallelogram because only one pair of sides is parallel. CONFIDENTIAL

Study these two figures (squares). How are they alike? Let’s start with Congruence 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

Two polygons are congruent if they are the same size and shape that is, if their corresponding angles and sides are equal. b° 90° a° b° 90° a° If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called Congruent: CONFIDENTIAL

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. is the sign of congruency. CONFIDENTIAL

Congruence of triangles A triangle has three sides and three angles. If two triangles are congruent, then the sides and angles that match are called corresponding parts. A B C D F E Let's look at the corresponding parts of triangles ABC and DFE. Angle A corresponds to angle D. Angle B corresponds to angle F. Angle C corresponds to angle E. CONFIDENTIAL

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

These triangles are congruent. Name the corresponding parts. 90° 30° A B C X Y Z What is the measure of angle X? What is the measure of angle Y? CONFIDENTIAL

A B C X Y Z Side AB side XY. Angle AB Angle XY. Side BC side YZ. 90° 30° A B C X Y Z Side AB side XY. Angle AB Angle XY. Side BC side YZ. Angle BC Angle YZ. Side CA side ZX. Angle CA Angle ZX. Measure of angle X = 30° Measure of angle Y = 60° CONFIDENTIAL

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Write whether these figures are congruent. Assignments Write whether these figures are congruent. 1) 2) 3) 4) CONFIDENTIAL

These triangles are congruent. 120° 30° A B C X Y Z 4 cm 7 cm What is the measure of angle Z? What is the measure of side XY? What is the measure of side YZ? What is the measure of side ZX? CONFIDENTIAL

These rhombus are congruent. Name the corresponding parts of the following. A B C D W X Y Z side AD side XY Angle A Angle Y CONFIDENTIAL

We will learn about Congruency today. Very Good! Let's Review We will learn about Congruency today. Two polygons are congruent if they are the same size and shape that is, if their corresponding angles and sides are equal. b° 90° a° b° 90° a° If one shape can become another using Turns, Flips and/or Slides, then the two shapes are called Congruent: CONFIDENTIAL

Congruent Angles have the same angle in degrees. Review 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

Congruence of triangles Review Congruence of triangles A triangle has three sides and three angles. If two triangles are congruent, then the sides and angles that match are called corresponding parts. A B C D F E Let's look at the corresponding parts of triangles ABC and DFE. Angle A corresponds to angle D. Angle B corresponds to angle F. Angle C corresponds to angle E. CONFIDENTIAL

Side AB corresponds to side DF. Review 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

These triangles are congruent. Name the corresponding parts. Review These triangles are congruent. Name the corresponding parts. 90° 30° A B C X Y Z What is the measure of angle X? What is the measure of angle Y? CONFIDENTIAL

A B C X Y Z Side AB side XY. Angle AB Angle XY. Side BC side YZ. Review 90° 30° A B C X Y Z Side AB side XY. Angle AB Angle XY. Side BC side YZ. Angle BC Angle YZ. Side CA side ZX. Angle CA Angle ZX. Measure of angle X = 30° Measure of angle Y = 60° CONFIDENTIAL

See you in the next session. You have done a nice job. See you in the next session. CONFIDENTIAL