Congruency and Similarity

Congruent shapes

shapes that are identical in side lengths and angles

Vertex

where two sides meet, such as the corner of a triangle

congruency

which sign is this for?

Tick marks

a small line drawn on the sides of identical triangles

arcs

curved lines that indicate that two angles are the same

SSS

all sides are equal

SAS

two sides and the included angle are equal

ASA

two angles and the included side are equal

RHS

for right-angled triangles. Hypotenuse and one other side are equal.

360

The sum of angles at a point

180

the sum of the interior angles of a triangle

supplementary angles

• The sum of the angles on a straight line is 180

complementary angle

The sum of the angles in a right angle is 90

equal

vertically opposite angles are

supplementary

If there are parallel lines, co-interior angles are ________ (a + b = 180)

equal

If there are parallel lines, corresponding angles are ______ (a = b)

equal

If there are parallel lines, alternate angles are _______ (a = b)

equilateral triangle

This follows Theorem 2 which states that each interior angle of an equilateral triangle is equal

opposite interior angle

Theorem 3: The exterior angle of a triangle is equal to the sum of the ________________

isosceles triangle

this is a triangle whose lengths of two sides are equal but the third is not equal

Similar shapes

Have the same shape but different sizes, and their corresponding sides are proportional

scale factor

the number you multiply by to get from one shape to a similar shape

ratio

compares two quantities, showing how many times one value contains or is contained within another

similar triangles

two triangles that have the same shape but may differ in size

AAA

• If all 3 angles in 2 or more triangles are the same, then the triangles will be similar

• The length of the sides of the triangles do not matter

SSS

• If all 3 pairs of corresponding sides are in the same ratio, the triangles are similar.

• That ratio is the scale factor between the triangles

SAS

• If two sides of one triangle are in the same ratio as two sides of another triangle and the included angle between those sides is equal, the triangles are similar

quadrilaterals

Shapes that have:

• four sides (edges)

• four vertices (corners)

• interior angles that ass to 360

congruent quadrilaterals

all sides, all angles are equal

similar quadrilaterals

all angles are equal, side in same position