tests for rhombi - mrs. stapp's math...
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Geo 6.5-6.6
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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
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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
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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
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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
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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
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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
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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
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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
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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
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2/13/14