## Let’s start by looking at the properties of all various types of quadrilaterals

A quadrilateral is any type of closed four-sided figure.

You are watching: What is the measure of a quadrilateral Tright here are two kinds of quadrilaterals: concave and convex.

A concave quadrilateral has a component that goes right into the shape:  All convex quadrilaterals have actually 4 sides (edges), four corners (vertices) and four interior angles that amount to ???360^circ???.

Here are some special types of convex quadrilaterals and their properties:

Trapezium

No pairs of parallel sides and also no congruent sides Kite

Has two pairs of nearby congruent sides

Has a pair of oppowebsite congruent angles

Diagonals cross to create appropriate angles and among the diagonals bisects the various other (cuts it in half) Isosceles trapezoid

Has exactly one pair of opposite parallel sides

Non-parallel sides have equal lengths

Base angles are congruent

Diagonals are congruent

Parallelogram

Two pairs of oppowebsite parallel sides

Opposite sides are equal lengths

Oppowebsite angles are congruent

???mangle 1=mangle 3???

???mangle 2=mangle 4???

Consecutive angles are supplementary

???mangle 1+mangle 2=180^circ???

???mangle 2+mangle 3=180^circ???

???mangle 3+mangle 4=180^circ???

???mangle 4+mangle 1=180^circ???

Diagonals bisect each other (cut each other in half)

Rectangle

Two pairs of oppowebsite parallel sides

Opposite sides are equal

All angles are best angles (???90^circ???)

Diagonals bisect each various other (reduced each other in half)

Diagonals are congruent

Rhombus/Diamond

Two pairs of opposite parallel sides

All sides are equal lengths

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals are perpendicular bisectors each various other (cut each other in fifty percent and also develop right angles)

Square

Two pairs of oppowebsite parallel sides

All angles are ideal angles

All sides are equal length

Diagonals bisect each various other (cut each other in fifty percent and develop appropriate angles)

## Solving for steps in a parallelogram and a trapezoid

Example

What is the value of ???x??? in the parallelogram?

Angles ???A??? and ???B??? are consecutive angles in a parallelogram (they’re beside each various other, not across the number from one another), so they’re supplementary. Because ???mangle A=102^circ??? and ???mangle B=44^circ +4x???, we have the right to say

???mangle A+mangle B=180^circ???

???102^circ+44^circ+4x=180^circ???

???146^circ+4x=180^circ???

???4x=34^circ???

???x=8.5^circ???

Tright here are 2 types of quadrilaterals: concave and convex.

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A concave quadrilateral has actually a part that goes right into the form, while

A convex quadrilateral has angles all on the exterior corners of the form.

Example

The figure below is a trapezoid. What is the meacertain of ???KN??? if ???KN=5x+2??? and ???IG=4x+20????

The side lengths of ???KG??? and also ???IN??? are noted as being the very same size, which implies this is an isosceles trapezoid. The diagonals of an isosceles trapezoid are congruent, which means that ???KN=IG???. Because of this,

???KN=IG???

???5x+2=4x+20???

???5x=4x+18???

???x=18???

Then the measure of ???KN??? need to be

???KN=5x+2???

???KN=5(18)+2???

???KN=92???