Lesson 5 Proving Quadrilaterals Are Congruent Quadrilateral A

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Lesson 5: Proving Quadrilaterals Are Congruent

Lesson 5: Proving Quadrilaterals Are Congruent

Quadrilateral - A four-sided polygon Polygon – A plane figure that meets the following

Quadrilateral - A four-sided polygon Polygon – A plane figure that meets the following conditions: • Closed (has no openings) • All straight segments • Does not cross over itself.

Polygons are named by the number of sides they have. • • • 3

Polygons are named by the number of sides they have. • • • 3 – Triangle 4 – Quadrilateral 5 – Pentagon 6 – Hexagon 7 – Heptagon • • • 8 - Octagon 9 - Nonagon 10 – Decagon 12 – Dodecagon 15 - Pentadecagon

Polygons can be described as convex or concave. • Convex – no line that

Polygons can be described as convex or concave. • Convex – no line that contains a side of the polygon also contains a point in the interior of the polygon. • Concave – A polygon that is not convex.

• A REGULAR polygon is one that is equalilateral and equiangular. • A

• A REGULAR polygon is one that is equalilateral and equiangular. • A DIAGONAL is a segment that joins two non-consecutive vertices.

Theorems of Quadrilaterals Interior Angles of Quadrilateral – The sum of the interior angles

Theorems of Quadrilaterals Interior Angles of Quadrilateral – The sum of the interior angles of a quadrilateral is ______. We know that the sum of the interior angles of a triangle is _______. A quadrilateral can be divided into two triangles; therefore the sum of the interior angles is _____.

Parallelogram: A quadrilateral with both pairs of opposite sides parallel.

Parallelogram: A quadrilateral with both pairs of opposite sides parallel.

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its opposite sides

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its opposite sides are congruent. Q P R S

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its opposite angles

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its opposite angles are congruent. Q P R S

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its consecutive angles

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Q P R S

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its diagonals bisect

Theorems of Parallelograms: • If a quadrilateral is a parallelogram, then its diagonals bisect each other. Q P R S

Let’s practice: F Ex: 1 G K J H

Let’s practice: F Ex: 1 G K J H

So, how do I prove a quadrilateral is a parallelogram? • 1. If the

So, how do I prove a quadrilateral is a parallelogram? • 1. If the opposite sides of a quadrilateral are congruent, then it’s a parallelogram. • 2. If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram. • 3. If an angle is supplementary to both its consecutive angles, then it is a parallelogram.

So, how do I prove a quadrilateral is a parallelogram? (cont) • 4. If

So, how do I prove a quadrilateral is a parallelogram? (cont) • 4. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. • 5. If one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram.

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