1. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides

2. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent

3. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent

4. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex A C B D

5. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E

6. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : If AD = 14, what is the measure of EB ? 60°

7. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : If AD = 14, what is the measure of EB ? SOLUTION : With angle ADE = 60 degrees we have a 30 – 60 – 90 triangle. So segment EB = Segment ED which is half of AD. 60°

8. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : If AD = 14, what is the measure of EB ? SOLUTION : With angle ADE = 60 degrees we have a 30 – 60 – 90 triangle. So segment EB = Segment ED which is half of AD. ED = 7 60°

9. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : What is the measure of angle ECD ? 60°

10. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : What is the measure of angle ECD ? SOLUTION : Again we have a 30 – 60 – 90 triangle. So angle DAC = 30 degrees. 60°

11. Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides - opposite angles are congruent - diagonals bisect the angles at the vertex - diagonals bisect each other and are perpendicular A C B D E 14 EXAMPLE : What is the measure of angle ECD ? SOLUTION : Again we have a 30 – 60 – 90 triangle. So angle DAC = 30 degrees. So angle ECD would also be 30 degrees. 60°

12. Polygons – Rhombuses and Trapezoids Trapezoid - two parallel sides that are not congruent D A B C ║

13. Polygons – Rhombuses and Trapezoids Trapezoid - two parallel sides that are not congruent D A B C ║ - these parallel sides are called bases - non-parallel sides are called legs base 1 base 2 leg

14. Polygons – Rhombuses and Trapezoids Trapezoid - two parallel sides that are not congruent D A B C ║ - these parallel sides are called bases - non-parallel sides are called legs base 1 base 2 leg - there are two pairs of base angles

15. Polygons – Rhombuses and Trapezoids Trapezoid - two parallel sides that are not congruent D A B C ║ - these parallel sides are called bases - non-parallel sides are called legs base 1 base 2 leg - there are two pairs of base angles - diagonal base angles are supplementary

16. Polygons – Rhombuses and Trapezoids Trapezoid - two parallel sides that are not congruent D A B C ║ - these parallel sides are called bases - non-parallel sides are called legs base 1 base 2 leg - there are two pairs of base angles - diagonal base angles are supplementary - base angles that share a leg are also supplementary

17. Polygons – Rhombuses and Trapezoids Isosceles Trapezoid - has all the properties of a trapezoid - legs are congruent - base angles are congruent D AB C

18. Polygons – Rhombuses and Trapezoids Isosceles Trapezoid - has all the properties of a trapezoid - legs are congruent - base angles are congruent - diagonals have the same length D AB C

19. Polygons – Rhombuses and Trapezoids Median of a Trapezoid - parallel with both bases - equal to half the sum of the bases - joins the midpoints of the legs D AB C XY

20. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the median length ? 20 28

21. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the median length ? 20 28 24

22. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : If AD = 18, what is the measure of AX ? 18 X Y

23. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : If AD = 18, what is the measure of AX ? 18 X Y The median joins the midpoints of the legs

24. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : ABCD is an isosceles trapezoid. If angle DAB = 110°, what is the measure of angle ABC ?

25. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : ABCD is an isosceles trapezoid. If angle DAB = 110°, what is the measure of angle ABC ? 110° -base angles are congruent in an isosceles trapezoid

26. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the length of side AB? ? 50 Y X 40

27. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the length of side AB? ? 50 Y X 40

28. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the length of side AB? ? 50 Y X 40

29. Polygons – Rhombuses and Trapezoids Let’s try some problems… D AB C EXAMPLE : What is the length of side AB? ? 50 Y X 40