Polygons: Triangles and Quadrilaterals Lesson 4.5 Polygons: Triangles and Quadrilaterals pp. 144-149

Objectives: 1. To classify triangles by type of angles and number of congruent sides. 2. To classify quadrilaterals by types of angles, lengths of sides, and pairs of parallel opposite sides.

Definition An acute triangle is a triangle with three acute angles. A right triangle is a triangle with a right angle. An obtuse triangle is a triangle with an obtuse angle.

Acute triangle Right triangle Obtuse triangle

Definition A scalene triangle is a triangle with no congruent sides. An isosceles triangle is a triangle with at least two congruent sides. An equilateral triangle is a triangle with 3 congruent sides.

Scalene triangle Isosceles triangle Equilateral triangle

The two congruent sides of an isosceles triangle are called legs The two congruent sides of an isosceles triangle are called legs. The other side is called the base. The angles formed by the base and legs are called base angles. The angle formed by the two legs is called the vertex angle.

A B C

To classify quadrilaterals, you must know about opposite and consecutive sides and angles.

opposite sides consecutive sides

opposite angles consecutive angles

Definition A trapezoid is a quadrilateral with a pair of parallel opposite sides. A parallelogram is a quadrilateral with two pairs of parallel opposite sides. A rectangle is a parallelogram with four right angles.

Definition A rhombus is a parallelogram with four congruent sides. A square is a rectangle with four congruent sides (or a rhombus with four congruent angles).

not parallel parallel Trapezoid

Parallelogram

Rectangle

Rhombus

Square

1. A trapezoid is a parallelogram. True/False 1. A trapezoid is a parallelogram. False

2. A parallelogram is a trapezoid. True/False 2. A parallelogram is a trapezoid. True

3. All squares are trapezoids. True/False 3. All squares are trapezoids. True

4. No rectangle is a rhombus. True/False 4. No rectangle is a rhombus. False

5. An equilateral quadrilateral is a rhombus. True/False 5. An equilateral quadrilateral is a rhombus. True

6. All rectangles are parallelograms. True/False 6. All rectangles are parallelograms. True

7. A rhombus is a rectangle. True/False 7. A rhombus is a rectangle. False

Homework pp. 147-149

►A. Exercises Classify each triangle by angle measure and by side lengths. 1.

►A. Exercises Classify each triangle by angle measure and by side lengths. 3.

►A. Exercises Classify each triangle by angle measure and by side lengths. 5.

17. equiangular quadrilateral ►B. Exercises Give another name for each. 17. equiangular quadrilateral

19. regular quadrilateral ►B. Exercises Give another name for each. 19. regular quadrilateral

►B. Exercises Express the given quantity using the values in the diagram. 23. QR Q 4 P x R

■ Cumulative Review Express each quantity. 28. One angle of a linear pair has measure x. Express the other angle’s measure.

■ Cumulative Review Express each quantity. 29. If x + 23 is the measure of one angle, find its complement.

■ Cumulative Review Write an equation and solve. 30. One angle measures 46° more than its complement. Find the measures.

■ Cumulative Review Write an equation and solve. 31. Find the measures of two supplementary angles if one is 15° more than twice the other.

■ Cumulative Review Write an equation and solve. 32. Suppose that C-P-D. If CD = 152 inches and PC is 4 inches more than 3 times PD, find the lengths.