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Presentation transcript:

11/16

1. EQ: What triangle properties can I use to solve for the missing information?

1. 2. What is the name of the theorem you used to solve this problem?

Exterior Angle Theorem The exterior angle is equal to the sum of the remote interior angles

Triangle Sum Theorem The sum of the interior angles of a triangle always add up to 180 degrees

Angle Relationships What is the relationship between… Corresponding angles? Alternate Exterior Angles? Alternate Interior Angles? Same Side Interior Angles?

Vertical Angles Find m∠1 if m∠1 = 13x + 7 and m∠3= 7x+49 Opposite angles formed by two intersecting lines are congruent Find m∠1 if m∠1 = 13x + 7 and m∠3= 7x+49

Similar Triangles What do we know about similar triangles??

Similar Triangles What are my coordinates for <A? <B? <C? What transformations occurred to get ABC to DEF? Use the distance formula!

Similar Triangles Angles are congruent Corresponding sides are proportional Can we prove similarity? How? What proportional can we set up?

Similar Triangles

Similar Triangles Can we prove similarity? How? Name the triangles to show similarity (match corresponding angles) Set up a proportion to solve for x

Similar Triangles Can we prove similarity? How? Name the triangles to show similarity (match corresponding angles) Set up a proportion to solve for x

Example 1 Front: Height of person should say 2.5 inches We know both angles are congruent because it says “same time of day” which means I can assume the sun is hitting both at the same angle Back: The height of the lamppost is 15.75 feet. I know that the triangles are similar because there are two right angles and two other congruent angles. I can set up the proportion 6/18 = 5.25/x to solve for x.