Geometric Reasoning

Mahobe

The facts to learn

• Angles in a triangle add up to 180o

• Angles on a straight line add up to 180o

• Angles around a point add up to 360o

base ’s isos ∆ =∠

∠ sum quad

• Interior angles of a quadrilateral sum to 360o

opp ,∠ cyclic quad

• Opposite angles of a cyclic quadrilateral sum to 180o

Ext , of cyclic quad∠

• Exterior angle of a cyclic quad equals the opposite interior angle

vert opp s =∠

• Vertically opposite angles are equal

alt s // lines∠

• Alternate angles are equal if the lines are parallel

corr s // lines∠

• Corresponding angles are equal if the lines are parallel

Co-int s // lines∠

• Co-interior angles sum to 180o if the lines are parallel

• Exterior angles of a polygon add up to 360o

If the polygon is regular all exterior angles are the same size

• Exterior angles of a polygon add up to 360o

ext regular pentagon∠

• Exterior angles of a regular pentagon is 72o

Interior angles of a polygon with n sides sum to 180(n-2)

Find all the other angles in this figure

Vert opp angles

A triangle formed with 2 radii is isosceles

• The angle at the centre is twice the angle at the circumference.

When writing angles use 3 letters. The middle letter is where the angle is.

Find the angles u, v and wO Is the centre

O Is the centre

O Is the centre

O Is the centre

Find angle d

Calculate the size of angle ABC

Calculate angle CDE

Calculate the size of angle HIJ

Calculate the size of angle c

C = 96o,

• Co-int angle // lines• Corr angles // lines

• ORAngles on a lineOpp angles parallelogram

Calculate the size of angle VUW

Shape P is a regular pentagon and shape H is a regular heptagon. Calculate the size of angle CBD

Shape P is a regular pentagon and shape H is a regular heptagon. Calculate the size of angle CBD

The diagram gives the angles of a playground slide. Find angle XYZ.

Find the size of angles NMO and OPN

Find the size of angles NMO and OPN

Find the size of angles PRQ and PSQ

O

O

XBC 90 Rad perp. tang

CBA 20 Angles on a line

CAB 20 Base angles isos triangle

XCB 40 Ext angle = sum opp int angles

CXB 50 Angle sum triangle

O Is the centre of the circle.Calculate the size of angle BCD

O Is the centre of the circle.Calculate the size of angle WYX

Similar triangles

ABC is an isosceles triangle.O is the centre of the circle.

Calculate the size of angles BAC and ODC

Calculate the size of angles x and y.

.

O is the centre of the circle.Calculate the size of angle BAC.

.

KNML is cyclic as the opposite angles sum to 180.

O is the centre of the circle.Prove angle CBY = angle CAB

angle CBY = angle CAB