Geometric Reasoning Mahobe. The facts to learn Angles in a triangle add up to 180 o.
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Transcript of Geometric Reasoning Mahobe. The facts to learn Angles in a triangle add up to 180 o.
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