6808628
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Mind Map by Lester Stoffels, updated more than 1 year ago
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Similarity and congruency
- Similarity
- Similar figures have the same
shape but can be different sizes
- It can either be an enlargement or
reduction
- It can either be an enlargement or
reduction
- Two polygons are similar
if:
- Their corresponding
angles are equal
(matching angles)
- Their corresponding
sides are in the same
proportion
- Their corresponding
angles are equal
(matching angles)
- The symbol for similar is
|||
- If two triangles have equal
corresponding angles, their
corresponding sides are in proportion
- If two triangles have corresponding sides in
proportion, corresponding angles are equal
- You have to put the triangle in the order
that it corresponds with the other triangle
to find out whether it is similar
- Similar figures have the same
shape but can be different sizes
- Congruency
- To prove congruency
compare, sides and
anlges.
- Congruent means identical
and equal in all respects (2
triangles must be compared)
- There are 4 cases of
congruency
- 1. If three sides of a triangle are respectively
equal to the three sides of the other triangle
then the two triangles are congruent (SSS)
- 2. If two sides and included angle of a triangle is
respectively equal to the two sides and the included
angle of another triangle ten they are congruent (SAS)
- 3.If two angles and one side of one
triangle are respectively equal to two
angles and the corresponding side of
another triangle, they are congruent
(AAS or ASA)
- 4.If the hypotenuse and one side of a right-angled triangle are
respectively equal to the hypotenuse and one side of another
right-angled triangle, they are congruent (RHS)
- RHS - Right-angle, hypotenuse &
side
- RHS - Right-angle, hypotenuse &
side
- 4.If the hypotenuse and one side of a right-angled triangle are
respectively equal to the hypotenuse and one side of another
right-angled triangle, they are congruent (RHS)
- 3.If two angles and one side of one
triangle are respectively equal to two
angles and the corresponding side of
another triangle, they are congruent
(AAS or ASA)
- 2. If two sides and included angle of a triangle is
respectively equal to the two sides and the included
angle of another triangle ten they are congruent (SAS)
- 1. If three sides of a triangle are respectively
equal to the three sides of the other triangle
then the two triangles are congruent (SSS)
- The symbol for congruency
->
- To prove congruency
compare, sides and
anlges.
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