Geometry: Similar Triangles

1
Geometry Similar Triangles
2
MA.912.G.2.6 Use coordinate geometry to prove
properties of congruent, regular and similar
polygons, and to perform transformations in the
plane

• Block 29

3
Congruent and similar triangles
4
Congruent and similar triangles

• Review of definitions, properties and theorems
  of congruent and similar triangles

5
Congruent and similar triangles and geometric
transformations
6
Geometric transformations of triangle
7
Examples of transformations reflection
8
Examples of transformations dilation
9
Examples of transformations translation by a
vector
10
Examples of transformations rotation
11
Examples of transformations reflection at a point
12
Answers to exercises

• Rotation ex1.ggb
• Reflection about a line ex2.ggb
• Translation by vector ex3.ggb
• Scaling ex4.ggb

13
Congruent and similar triangles and coordinate
geometry
14
Congruent triangles

• SSS
• If three sides of one triangle are congruent to
  three sides of a second triangle, the two
  triangles are congruent.
•  ASA
• If two angles and the included side of one
  triangle are congruent to two angles and the
  included side of another triangle, the triangles
  are congruent.

15
Congruent triangles

• SAS
• If two sides and the included angle are congruent
  to two sides and the included angle of a second
  triangle, the two triangles are congruent.
• AAS
• If two angles and a non included side of one
  triangle are congruent to two angles and the
  corresponding non-included side of another
  triangle, the two triangles are congruent.

16
Congruent triangles

• Hyp-S
•  
• If the hypotenuse and the leg of one right
  triangle are congruent to the corresponding parts
  of the second right triangle, the two triangles
  are congruent

17
Similar triangles

• Similar triangles have the same shape, but the
  size may be different.
• Two triangles are similar if
• two pairs of corresponding angles are congruent
  (therefore the third pair of corresponding angles
  are also congruent).
• OR
• the three pairs of corresponding sides are
  proportional.

18
Similar triangles

• To find out if triangles given in coordinate
  geometry are similar you can check any of the
  properties using coordinate geometry like
  distance formula

19
Guided exercise

• Use graphic paper for Question 1 in handout

20
Final remarks and discussion

• Discuss in groups how you can teach topics in
  this section using web-based educational
  resources designed to reinforce learning ?
• Identify effective strategies for teaching
• Share your ideas in class discussion
• Answer the Question 2