Maths Properties of Shapes Year One Maths | Year 5 | Properties of Shapes | Use the Properties of Rectangles to Find Missing Facts and Angles | Lesson 2 of 2: Rectangle Relations
Rectangle Relations
Aim I can use the known properties of rectangles to find missing lengths and angles. Success Criteria I can find missing lengths of quadrilaterals. I can find missing angles of quadrilaterals.
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Which 3D shape does this net represent? Which Net? Which 3D shape does this net represent?
Discuss the similarities and differences between these rectangles.
Rectangles A rectangle has four sides. 90° 90° 90° 90° A rectangle has four sides. Opposite sides of a rectangle are the same length (congruent). Opposite sides of a rectangle are parallel. 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 Square 4 equal parallel sides. 4 right angles (90°).
2 pairs of parallel sides. Quadrilaterals Rectangle 2 pairs of parallel sides. 4 right angles (90°).
Diagonally opposite angles are equal. Quadrilaterals Rhombus All sides are equal. Diagonally opposite angles are equal.
Quadrilaterals Parallelogram 2 pairs of equal parallel sides Diagonally opposite angles are equal
1 pair of sides are parallel. Quadrilaterals Irregular Trapezium 1 pair of sides are parallel.
Horizontally opposite angles are equal. Quadrilaterals Kite Horizontally opposite angles are equal. 2 pairs of equal sides.
Quadrilaterals Isosceles Trapezium 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.
Do all interior angles in quadrilaterals measure 360° in total? Quadrilateral Angles Yes! Do all interior angles in quadrilaterals measure 360° in total? 360° 360° 360° 100° 120° 100° 90° 90° 100° 100° 60° 80° 90° 90° 60° Irregular Trapezium Square Kite 360° 360° 100° 360° 115° 65° 115° 115° 80° 80° 65° 65° 100° 65° 115° Isosceles Trapezium Rhombus Parallelogram
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. ? ? 115° 65°
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°. 65° 115° 115° 65°
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! 65° 115° 115° 65°
Missing Angles and Lengths
True or False Angles? True False The missing angle is 108°. 90° 108° ? 54° True False
True or False Angles? True False The missing angle is 104°. ? 104° 76° 104° True False
True or False Angles? True False The missing angle is 95°. 90° 90° ?
True or False Angles? True False The missing angle is 120°. 120° 60°
True or False Angles? True False The missing angle is 60°. 115° 115° 65° ? True False
Aim I can use the known properties of rectangles to find missing lengths and angles. Success Criteria I can find missing lengths of quadrilaterals. I can find missing angles of quadrilaterals.