Similar Triangles OBJECTIVES: To use the To use similarity to find indirect measurements BIG IDEA: Visualization ESSENTIAL UNDERSTANDINGS Triangles can be shown to be similar based on the relationship of two or three pairs of corresponding parts. Similar triangles can be used to find unknown measurements MATHEMATICAL PRACTICE Construct viable arguments and critique the reasoning of others Similar Triangles

Similar Triangles The definition of similar triangles involves a complicated set of conditions. Postulates and theorems about similarity can provide a shortcut to proving triangles similar. Similar triangles can be used for indirect measurement in a variety of circumstances. Similar triangles are also part of the basic idea of proportionality, which extends through all areas of Geometry. Proving statements in Geometry helps students understand how to develop logical arguments in other areas of their lives. You can show that two triangles are similar when you know the relationships between only two or three pairs of corresponding parts.

Similarity Postulate and Theorems Angle-Angle Similarity Postulate: If _______________ angles of one triangle are ____________________ to two angles of another triangle, then the two triangles are ____________________ Side-Angle-Side Similarity Theorem: If an _______________ of one triangle is ____________________ to an angle of a second triangle, and the _______________ that include the two angles are ____________________, then the triangles are ____________________ Side-Side-Side Similarity Theorem: If the ____________________ sides of two triangles are ____________________, then the triangles are ___________________

EX 1: Are the two triangles similar? How do you know? Similarity Statement: B) Similarity Statement:

EX 2: Are the two triangles similar? How do you know? Similarity Statement: B) Similarity Statement:

EX 3: Are the two triangles similar? How do you know? Similarity Statement: B) Similarity Statement:

EX 4: Are the two triangles similar? How do you know? Similarity Statement: B) Similarity Statement:

EX 5: Are the two triangles similar? How do you know? Similarity Statement: B) Similarity Statement:

MATH IXL P7 Mastery Level

Indirect Measurement Sometimes you can use similar triangles to find lengths that cannot be measured easily using a ruler or other measuring devices. You can use indirect measurement to find lengths that are difficult to measure directly.

EX: The triangles are similar. Find the value of x 1)

EX: The triangles are similar. Find the value of x 2)

EX: The triangles are similar. Find the value of x 3)

EX: The triangles are similar. Find the value of x 4)

EX: The triangles are similar. Find the value of x 5)

MATH IXL P5 Mastery Level