Transcript Geometry Sections 6.4 and 6.5

Geometry
Sections 6.5
Prove Triangles Similar by SSS
and SAS
Side-Side-Side (SSS) Similarity
Theorem (Theorem 6.2)
• If the corresponding
side lengths of two
triangles are
proportional, then
the triangles are
similar
Example 1: Is either ∆ DEF or ∆ GHJ similar to ∆ ABC?
Step 1: Compare ∆ ABC and ∆ DEF by finding ratios of corresponding side
lengths.
Shortest sides
Longest sides
Remaining sides
Step 2: Compare ∆ ABC and ∆ GHJ by finding ratios of corresponding side
lengths.
Shortest sides
Longest sides
Remaining sides
Example 2:
Find the value of x that makes
triangle ABC ~ triangle DEF.
Example 2 (Con’t):
Find the value of x that makes
triangle ABC ~ triangle DEF.
Side-Angle-Side (SAS) similarity
Theorem (Theorem 6.3)
• If an angle of one triangle
is congruent to an angle of
a second triangle and the
lengths of the sides
including these angles are
proportional, then the
triangles are similar
Use the SAS Similarity Theorem
Example 4:
Is ∆ FDM ~ ∆AVQ?
YES
Example 5:
Is ∆ GHK ~ ∆ NMK?
YES
Examples
• Page 391-393:
4-10 All, 15, 18-23