Geometric Reasoning Mahobe.

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Presentation transcript:

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

Find the angles u, v and w O 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 OR Angles on a line Opp angles parallelogram

Calculate the size of angle VUW

Shape P is a regular pentagon and shape H is a regular heptagon 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 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

XBC 90 Rad perp. tang CBA 20 Angles on a line CAB 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 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