Properties of Other Quadrilaterals Students will be able to… Identify and use the properties of rectangles, squares, rhombuses, kites, and trapezoids.

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Presentation transcript:

Properties of Other Quadrilaterals Students will be able to… Identify and use the properties of rectangles, squares, rhombuses, kites, and trapezoids

The following quadrilaterals have perpendicular diagonals: Rhombus Square Kite

The following quadrilaterals have opposite angles that are bisected: Rhombus Square

Example: Find the measures of the numbered angles in the rhombus °

The figure below is a rhombus. Find TQ, TP, and SQ.

The following quadrilaterals have congruent diagonals Rectangle Square Isosceles Trapezoid

EXAMPLE BD=5y-7 and AC = y + 5. Find the value of y and the length of BE. E

EXAMPLE: If BD= 2x+10 and AC=x+15, find x and the length of the diagonals.

TRAPEZOID LEG BASE ANGLES The 2 parallel sides are the bases The 2 non-parallel sides are the legs A B C D Name the following: Bases: Legs: 2 Pairs of Base Angles:

The following quadrilaterals have exactly one pair of opposite parallel sides Trapezoid Isosceles Trapezoid The following quadrilaterals have exactly one pair of opposite congruent sides: Isosceles Trapezoid

Theorem: The base angles of an isosceles trapezoid are congruent A B C D Example- Find x given the following angle measures:

The following quadrilaterals have exactly one pair of opposite congruent angles Kite

Example: Find the measures of the numbered angles. 46° 3 2 1

44°112° 1 2 FIND THE MEASURE OF THE MISSING ANGLES., assign x to represent each measure. So equation will be: x+x = 360 How many degrees in a quadrilateral? What do we know about the relationship between angles 1 and 2?

2 angles that share a leg in a trapezoid are supplementary because they are same-side interior angles.

The following is an isosceles trapezoid. The measure of angle A= 110. Find the measures of the other 3 angles.

Midsegment (Median) of a Trapezoid Joins the midpoints of the nonparallel sides Is parallel to the bases Its length is ½ the sum of the bases MN || BC MN || AD MN = ½(BC+AD)

° 108° Find the following: EF:

Find x: 8 12 x