tests for rhombi - mrs. stapp's math...

Geo 6.5-6.6

1

2/13/14

6.5 Rhombi: Definition: A rhombus is a parallelogram with all four sides congruent.

Properties/Theorems:1. If a parallelogram is a rhombus, then its diagonals are perpendicular.

2. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

1. If the diagonals of a parallelogram are perpendicular, then it is a rhombus.

2. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

3.If one pair of consecutive sides of a parallelogram are congruent, then it is a rhombus.

Tests for Rhombi

A

B

C

D

6.4-6.6: Rectangles, Squares, Rhombi, Trapezoids

Geo 6.5-6.6

2

2/13/14

The diagonals of rhombus FGHJ intersect at K.

a. If FK = 5 and FG = 13, find KJ.

b. If , find y.

a. b. 6y + 7 = 9y -5

Geo 6.5-6.6

3

2/13/14

Squares: Definition: A square is a parallelogram with four congruent sides and four right angles.

Test for a square:1. If a quadrilateral is both a rectangle and a rhombus, then it is a square.

Geo 6.5-6.6

4

2/13/14

Given the set of vertices, determine whether parallelogram BEFG is a rhombus, a rectangle, or a square. List all that apply. Explain.

B(-9, 1), E(2, 3), F(12, -2), G(1, -4)

What do you need to know?

squares-4 right angles, all sides congruent

rhombus-all sides congruent

rectangle-4 right angles

What can you prove???

Geo 6.5-6.6

5

2/13/14

Parallelograms

Rectangles

RhombiSquares

Fill in the Venn Diagram with the options below.

Geo 6.5-6.6

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2/13/14

Trapezoids:Definition: A trapezoid is a quadrilateral with exactly one pairof parallel sides.

Properties/Theorems:1. If a trapezoid is isosceles, then each pair of base angles is congruent.

2. If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.

3. A trapezoid is isosceles if and only if its diagonals are congruent.

Geo 6.5-6.6

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2/13/14

Midsegment of a Trapezoidthe segment that connects the midpoints of the legs of a trapezoid

Trapezoid Midsegment Theorem

Geo 6.5-6.6

8

2/13/14

For the following trapezoids, use the Trapezoid Midsegment Theorem to find x.

1.

2.

28 + 16

2

Try this!

Geo 6.5-6.6

9

2/13/14

Kite:

Definition: A kite is a quadrilateral with exactly two pairs of consecutive congruent sides.

Properties/Theorems:1. If a quadrilateral is a kite, then its diagonals are perpendicular.

2. If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

Geo 6.5-6.6

10

2/13/14

If FGHJ is a kite, find

1.

2.

ABCD is a kite:

p.443 4a

<F is congruent to <H since <G is not congruent to <J

128 + 72 + x + x = 360

200 + 2x = 360

2x = 160

x=80

Try this!

Geo 6.5-6.6

11

2/13/14

Fill in the graphic organizer with these vocabulary words.

quadrilaterals isosceles trapezoid

parallelogram kite

rhombus

square

rectangle

trapezoid

Geo 6.5-6.6

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2/13/14

Assignment:

Monday 2/10/14: p 435(7-12, 22-33)

Weekend: 1. Copy/print notes 6.5-6.6

2. Complete problems in notes

3. p.444 (1-6)

Geo 6.5-6.6

13

2/13/14