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Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides

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

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Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides

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  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 B A C 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 B A E C D

  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 B A E 14 C 60° D EXAMPLE : If AD = 14, what is the measure of EB ?

  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 B A E 14 C 60° D 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.

  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 B A E 14 C 60° D 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

  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 B A E 14 C 60° D EXAMPLE : What is the measure of angle ECD ?

  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 B A E 14 C 60° D EXAMPLE : What is the measure of angle ECD ? SOLUTION : Again we have a 30 – 60 – 90 triangle. So angle DAC = 30 degrees.

  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 B A E 14 C 60° D 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.

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

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

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

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

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

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

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

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

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

  25. Polygons – Rhombuses and Trapezoids Let’s try some problems… 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 A B D C

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

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

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

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

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