Download Lesson 11.2 completed

Lesson 11.2:
1. Homework Discussion
2. Similar Triangles
3. Shortcuts
Warm Up #1:
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Copy ∆𝑅𝑂𝑌 onto graph paper.
Draw its dilation by a scale factor of 3.
Find any missing lengths and angle measures.
Determine the perimeter of each triangle.
What is the ratio of the perimeter of the dilated triangle
to the perimeter of the original triangle.
• Determine the area of each triangle.
• What is the ratio of the area of the dilated triangle to the
area of the original triangle.
Warm Up #2:
• Sketch two different equilateral triangles
∆𝐴𝐵𝐶 𝑎𝑛𝑑 ∆𝑋𝑌𝑍
• Are the corresponding angles congruent?
• Determine the ratios of the sides.
𝐴𝐵 𝐵𝐶 𝐴𝐶
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,
𝑋𝑌 𝑌𝑍 𝑋𝑍
• Are the ratios of the sides the same?
• Are the triangles similar?
• Check with the people near you. Did they have similar
triangles? Are your triangles similar to theirs?
Similar Triangles:
• From the previous lesson, we concluded that
polygons must have the following if they are
similar:
1. Congruent corresponding angles.
2. Proportional corresponding sides. (The ratio
of the corresponding sides must always be
the same.)
Today we will test for shortcuts.
The Angle-Angle (AA) Similarity
Conjecture:
• Based on Warm up #2, is AA a shortcut to proving
triangles similar?
• AA Similarity Conjecture: If _______ angles of one
triangle are congruent to _______ angles of another
triangle, then ______________________________
Practice #1:
• Determine if the triangles can be proved similar by AA. If so,
write a similarity statement.
Side-Side-Side Similarity Conjecture:
• Based on Warm Up #1, can we prove triangles are
similar by using the Side-Side-Side Similarity
Conjecture?
• SSS Similarity Conjecture: If the three sides of one
triangle are proportional to the three sides of
another triangle, then the two triangles are
_______________.
Practice #2:
• Determine if the triangles can be proved similar by SSS. If so,
write a similarity statement.
Side-Angle-Side:
• Also based on Warm Up #1, does it follow that we can
prove triangles are similar by using the SAS shortcut
method?
• SAS Similarity Conjecture: If two sides of one triangle are
proportional to two sides of another triangle and the
included angles are congruent, then the two triangles are
_______________.
Practice #3:
• Determine if the triangles can be proved similar by SAS. If so,
write a similarity statement.
Applying the Shortcuts – Example #4:
Applying the Shortcuts – Example #5:
Homework:
• P. 591-594: 1-6, 10, 20, **17