15 Properties of Quadrilaterals

Types of Quadrilaterals: Definitions and Properties

Chapter 15

Instructions:
Slides with information are not timed.
Slides with questions are timed with some being 1 minute and others being 3 minutes.
Recommended practice is suggested prior to each quiz section.

Quadrilaterals Defined

• A polygon with 4 sides

• All sides are straight

Types of quadrilaterals

• parallelogram

• rectangle

• square

• rhombus

• trapezoid

• isosceles trapezoid

• right trapezoid

• kite

• right kite

Parallelogram Definition

• Quad with opposite sides parallel (2 pairs)

Parallelogram Properties

• opposite angles are congruent

• opposite sides are congruent

• Consecutive angles are supplementary

• diagonals bisect each other

• Each diagonal splits the parallelogram into 2 congruent triangles.

Parallelogram practice can be found on page 215 in your Springboard workbook.
The next 8 slides are timed questions.

Multiple Choice

Which is NOT a property of a parallelogram?

• Diagonals bisect each other

• Diagonals are congruent

• Both pairs of opposite sides are parallel

• Both pairs of opposite angles are congruent

Multiple Choice

If AE = 2y and CE = y+5, what is the measure of AE?

• 10

• 5

• 2y

• y+5

Multiple Choice

If AE = 2y and CE = y+5, what is the measure of EC?

• 10

• 5

• 2y

• y+5

Multiple Choice

If DE = x+1 and BE = 3x-13, what is the measure of DB?

• 14

• 4x-12

• 7

• 16

Multiple Choice

If m∠D=(b+15)˚ and m∠C=(2b)˚, what is m∠A?

• (2b)˚

• (b+15)˚

• 55˚

• 110˚

Multiple Choice

If m∠D=(b+15)˚ and m∠C=(2b)˚, what is m∠B?

• (2b)˚

• (b+15)˚

• 55˚

• 110˚

Multiple Choice

If m∠D=(b+15)˚ and m∠C=(2b)˚, what is m∠C?

• (2b)˚

• (b+15)˚

• 55˚

• 110˚

Multiple Choice

If m∠D=(b+15)˚ and m∠C=(2b)˚, what is m∠D?

• (2b)˚

• (b+15)˚

• 55˚

• 110˚

Rectangle Definition

• Parallelogram with ALL angles being right angles

Properties of Rectangles

• diagonals bisect each other

• diagonals are congruent

• opposite sides are congruent

Rectangle practice can be found on page 220 in your Springboard workbook.
The next 5 slides are timed questions.

Multiple Select

Which of the following is true about the diagonals of a rectangle? Select all that are true.

• Diagonals bisect each other

• Diagonals are congruent

• Diagonal are perpendicular

• Diagonals bisect the angles

Multiple Choice

Given a rectangle. If m∠CBE=65˚, then what is m∠DAB?

• 65˚

• 90˚

• 25˚

• 50˚

Multiple Choice

Given a rectangle. If m∠CBE=65˚, then what is m∠BDC?

• 65˚

• 90˚

• 25˚

• 50˚

Multiple Choice

Given a rectangle. If m∠CBE=65˚, then what is m∠BDA?

• 65˚

• 90˚

• 25˚

• 50˚

Multiple Choice

Given a rectangle. If m∠CBE=65˚, then what is m∠CEB?

• 65˚

• 90˚

• 25˚

• 50˚

Square Definition

• Parallelogram with All 4 sides congruent and All 4 angles are right angles

• Rectangle with 4 congruent sides

• Rhombus for 4 right angles

Properties of Squares

• the diagonals bisect each other

• the diagonals are congruent

• The diagonals are perpendicular

• the diagonals bisect the angles of the square

The next 6 slides are timed questions.

Multiple Choice

Given a square. What is the m∠COB?

• 360˚

• 90˚

• 45˚

• 180˚

Multiple Choice

Given a square. What is the m∠CBO?

• 360˚

• 90˚

• 45˚

• 180˚

Multiple Choice

The diagonals of a square are

• parallel

• congruent

• perpendicular

• congruent and perpendicular

Multiple Choice

By definition, the 4 sides of a square are

• parallel

• congruent

• perpendicular

• not congruent

Drag and Drop

A square can be called a ​ ​ ​

Placeholder

but it cannot be called a ​

Placeholder

Drag these tiles and drop them in the correct blank above

rhombus

kite

pentagon

triangle

Drag and Drop

A square can be called a ​ ​ ​

Placeholder

but it cannot be called a ​

Placeholder

Drag these tiles and drop them in the correct blank above

rectangle

trapezoid

hexagon

pentagon

Rhombus Definition

• Parallelogram with ALL 4 sides congruent

Properties of a Rhombus

• opposite angles are congruent

• diagonals bisect each other

• diagonal bisect opposite angles

• diagonals are perpendicular

• diagonals are NOT congruent

• consecutive angles are supplementary

• a rhombus is a parallelogram

Rhombus practice can be found on page 220 in your Springboard workbook.
The next 5 slides are timed questions.

Multiple Choice

Which of the following are NOT true about diagonals of a rhombus?

• they are perpendicular

• they bisect each other

• they are congruent

Multiple Choice

If m∠BDC = 30˚, what is the m∠CDA?

• 30˚

• 60˚

• 120˚

• 90˚

Multiple Choice

If m∠BDC = 30˚, what is the m∠ACB?

• 30˚

• 60˚

• 120˚

• 90˚

Multiple Choice

If m∠BDC = 30˚, what is the m∠ABC?

• 30˚

• 60˚

• 120˚

• 90˚

Multiple Choice

If m∠BDC = 30˚, what is the m∠ABD?

• 30˚

• 60˚

• 120˚

• 90˚

Trapezoid Definition

• Quad with exactly 1 pair of parallel sides

Properties of a Trapezoid

• parallel sides are called bases

• "non-parallel" sides are called legs

• diagonals have no particular distinction.

• ALL 4 angles have different angle measures.

• Each pair of angles that share a leg are supplementary

Isosceles Trapezoid

• Quad with exactly 1 pair of parallel sides and 1 pair of congruent legs

Properties of an Isosceles Trapezoid

• same properties as a "trapezoid"....except:

• 2 pairs of congruent base angles

• diagonals are congruent

The next 7 slides are timed questions.

Multiple Choice

The diagonals of a trapezoid bisect each other.

• True

• False

Multiple Choice

The diagonals of an isosceles trapezoid are congruent.

• True

• False

Multiple Choice

The legs of an isosceles trapezoid are _____.

• parallel

• perpendicular

• congruent

• skew

Multiple Choice

Base angles of an isosceles trapezoid are _____.

• parallel

• perpendicular

• congruent

• supplementary

Math Response

If m∠B = 42˚ then to calculate the m∠A, you would type_________in a calculator.

Type answer here

Correct Answer: 180-42

Deg^°

Rad

Kite Definition

• Quad with 2 pairs of adjacent or consecutive sides congruent

Properties of a Kite

• 1 pair of opposite angles are congruent

• 1 diagonal is bisected

• diagonals are NOT congruent

• diagonals are perpendicular

Kite practice can be found on page 208 in your Springboard workbook.
The next 8 slides are timed questions.

Drag and Drop

Given kite JKLM, segment ​

Placeholder

bisects segment ​ ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

KL

LM

KM

JL

Multiple Choice

In the kite JKLM, segment KL is congruent to segment _____.

• JM

• KL

• KJ

• LM

Multiple Choice

In the kite JKLM, which diagonal bisects a pair of opposite angles?

• JL

• KM

• KJ

• LM

Multiple Choice

In the kite JKLM, which triangle is congruent to ΔJKM?

• ΔJLK

• ΔLKM

• ΔLKJ

• ΔKLM

Multiple Choice

In the kite JKLM, which angle is congruent to ∠JMK?

• ∠JLK

• ∠LKM

• ∠LMK

• ∠KLM

Multiple Choice

In the kite JKLM, which angle is congruent to ∠MJK?

• ∠JLK

• ∠MLK

• ∠LMK

• ∠KLM

Multiple Choice

In the kite JKLM, segment ML is congruent to segment _____.

• MJ

• KL

• KJ

• KM

Multiple Choice

In the kite JKLM, segment ML is congruent to segment _____.

• MJ

• KL

• KJ

• KM

Triangle Midsegment Definition

• Segment connecting 2 midpoints

Triangle Midsegment Properties

• midsegment is parallel to third triangle side

• midsegment bisects 2 sides of the triangle

• midsegment is half the length of the parallel side

Triangle Midsegment Theorem

• DE || BC

• DE = (1/2)BC

Triangle midsegment practice can be found on page 208 in your Springboard workbook.
The next 3 slides are a timed questions.

Multiple Choice

DE is a midsegment of triangle ABC. EC=6. BC=17. AD=4.

Find the measure of DE.

• 4

• 6

• 17

• 8.5

Multiple Choice

DE is a midsegment of triangle ABC. EC=6. BC=17. AD=4.

Find the measure of AE.

• 4

• 6

• 17

• 8.5

Multiple Choice

DE is a midsegment of triangle ABC. EC=6. BC=17. AD=4.

Find the measure of DB

• 4

• 6

• 17

• 8.5

Trapezoid Median
(or Midsegment) Definition

• Segment connecting midpoints of the legs

Trapezoid Median
(or Midsegment) Properties

• bisects both legs

• parallel to both bases

• length of median(midsegment) is half the sum of the bases

Trapezoid Median
(or Midsegment) Theorem

• The length of the median is the average of the bases.

Trapezoid practice can be found on page 212 in your Springboard workbook.
The next 3 slides are a timed questions.

Multiple Choice

BC=11. AD=15. EA=3. CF=4. Find the measure of BE.

• 3

• 5

• 4

• 11

Multiple Choice

BC=11. AD=15. EA=3. CF=4. Find the measure of FD.

• 3

• 5

• 4

• 11

Multiple Choice

BC=11. AD=15. EA=3. CF=4. Find the measure of EF.

• 15

• 13

• 4

• 11

This is everything you need to know to be able to complete SB 15.

Thank you