1. Polygons: Triangles and Quadrilaterals
Lesson 4.5
Polygons: Triangles and Quadrilaterals pp

2. 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.

3. 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.

4. Acute triangle
Right triangle
Obtuse triangle

5. 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.

6. Scalene triangle
Isosceles triangle
Equilateral triangle

7. 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.

8. A B C

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

10. opposite sides
consecutive
sides

11. opposite angles
consecutive
angles

12. 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.

13. 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).

14. not parallel
parallel
Trapezoid

15. Parallelogram

16. Rectangle

17. Rhombus

18. Square

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

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

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

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

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

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

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

26. Homework pp

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

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

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

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

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

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

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

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

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

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

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