lo i can use known properties of quadrilaterals to find missing … · quadrilateral angles do all...

Monday 22nd June 2020

LO I can use known properties of quadrilaterals to find missing lengths and angles

Quick recap - Shape Nets

Which 3D shape does this net represent?

Quick recap - Shape Nets

Which 3D shape does this net represent?

Quick recap - Shape Nets

Which 3D shape does this net represent?

Quick recap - Shape Nets

Which 3D shape does this net represent?

Quick recap - Shape Nets

Which 3D shape does this net represent?

Quick recap - Shape Nets

Which 3D shape does this net represent?

Rectangles

What similarities and differences can you see

looking at these rectangles?

Last week we learnt all about rectangles

90

°

90

°

90

°

90

°

• A rectangle has four sides.

• Opposite sides of a rectangle are the same length (congruent). This is

shown by matching short, straight lines.

• Opposite sides of a rectangle are parallel. This is shown by matching

arrows.

• A rectangle has four right angles.

• The angles of a rectangle are all congruent (the same size and

measure.)

• Opposite angles of a rectangle are congruent.

• The interior angles measure 360° in total.

Quadrilaterals

A rectangle is a quadrilateral.

A quadrilateral is a 4-sided, 2d shape.

All of the interior (inside) angles in a quadrilateral add up to 360°.

We are going to look at some other quadrilaterals today.

Quadrilaterals

4 equal parallel sides.

4 right angles (90°).

Square

Quadrilaterals

2 pairs of parallel sides.

4 right angles (90°).

Rectangle

Quadrilaterals

All sides are equal.

Diagonally opposite angles are equal.

Rhombus

Quadrilaterals

2 pairs of equal parallel sides

Diagonally opposite angles are equal

Parallelogram

Quadrilaterals

1 pair of sides are parallel.

Irregular Trapezium

Quadrilaterals

Horizontally opposite angles are equal.

2 pairs of equal sides.

Kite

Quadrilaterals

1 pair of sides are parallel.

1 pair of the sides are the same length.

The angles on either side of the parallel sides are equal.

Isosceles Trapezium

Quadrilateral Angles

Do all interior angles in these quadrilaterals measure 360° in total?

Irregular Trapezium Square Kite

ParallelogramRhombusIsosceles Trapezium

120

°

60° 80°

100

°

115

°

65°65°

115

°

90°90°

90°90°

100

°

100

°

100

°

60°

100

°

100

°

80°80°

115

°

65°

65° 115

°

Quadrilateral Angles

Do all interior angles in these quadrilaterals measure 360° in total?

Irregular Trapezium Square Kite

ParallelogramRhombusIsosceles Trapezium

120

°

60° 80°

100

°

115

°

65°65°

115

°

90°90°

90°90°

100

°

100

°

100

°

60°

100

°

100

°

80°80°

115

°

65°

65° 115

°

Yes!

Finding Missing Angles

We can use the known properties of quadrilaterals (and the known fact

that the interior angles of quadrilaterals always measure 360°) to find

missing angles in these shapes.

Step 1 – Think about the properties of the shape.

This shape is a rhombus.

I know that a rhombus has

diagonally opposite equal

angles.

??

65°115°

Finding Missing Angles

We can use the known properties of quadrilaterals (and the known fact

that the interior angles of quadrilaterals always measure 360°) to find

missing angles in these shapes.

Step 2 – Apply the known facts to the shape.

I can see that I have one of each of

the diagonal angles.

So I can reason that the missing

angles are 65° and 115°.

115°65°

65°115°

Finding Missing Angles

We can use the known properties of quadrilaterals (and the known fact

that the interior angles of quadrilaterals always measure 360°) to find

missing angles in these shapes.

Step 3 – Check that the total of the angles equals 360°.

115° + 115° + 65° + 65° = 360

I have found the missing angles!

115°65°

65°115°

Let’s put this learning to the test

1. Are these properties always (A), sometimes (S) or never true (N) for each

quadrilateral? Copy and complete the table using the right letter.

Let’s put this learning to the test

Find the missing lengths and angles of these quadrilaterals.

2. 3.

a) b)

a)b)

Let’s put this learning to the test

Find the missing lengths and angles of these quadrilaterals.

4. 5.

a)

b)

a)

b)

Let’s put this learning to the test

Find the missing lengths and angles of these quadrilaterals.

6. 7.

a)

b)

a)

b)

Let’s put this learning to the test

Find the missing lengths and angles of these quadrilaterals.

8.

9. Claudette says that the parallelogram with longer sides must have larger

angles. How will you explain her mistake?

Samira

Billy

Let’s see how you did

Answers

1.

2. a) 3.6cm

b) 90°

3. a) 90°

b) 4.5cm

Let’s see how you did

Answers

4. a) 104°

b) 5.5cm

5. a) 110°

b) 4cm

6. a) 115°

b) 3.5cm

7. a) 122°

b) 3cm

8. Samira is correct. We can use the information given to work out the missing

angle. The missing angle is 92°.

9. The lengths of the lines do not make any difference to the size of the angles.

Well done you have used known properties of quadrilaterals to

find missing lengths and angles!