Turn in homework you corrected on Monday. Pull out worksheet you started on Monday. A chicken farmer also has some cows for a

total of 30 animals, and the animals have 74 legs in all. How many chickens does the farmer have?

“By seeking and blundering we learn.” ― Johann Wolfgang von Goethe

Do Now

Look through your notebook to clarify any misunderstandings on the quiz/exit slips and to make sure you have a score for everything.

Turn in the homework from Tuesday. Pull out review from yesterday. Turn to the person next to you and come up

with one question you want to ask Miss Forsyth to start off our review.

“By seeking and blundering we learn.” ― Johann Wolfgang von Goethe

Do Now

Unit 3 Wrap-Up

Prove the triangle inequality theorem, and use it to make statements about the sides of triangles.

Describe the conditions for classifying triangles using the converse of the Pythagorean Theorem.

Prove the angle bisector theorem and perpendicular bisector theorem.

Today’s Objectives

Any side of a triangle is always shorter than the sum of the other two sides.

Triangle Inequality Theorem

What values of x make this triangle possible?

Pythagorean theorem If it’s a right triangle, a2+b2=c2. Converse If a2+b2=c2, then it’s a right triangle. If a2+b2>c2, Then it’s an acute triangle. If a2+b2<c2, Then it’s an obtuse triangle.

Classifying triangles with Pythagoras

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Triangle Angle Bisector Theorem

What would be the length of BD if CD were 3cm, CA were 6cm, and AB were 8 cm?

Using the Triangle Angle Bisector Theorem

A point is equidistant from the endpoints of a segment, if and only if it is on the perpendicular bisector of that segment.

If a point is equidistant from the endpoints of a segment then it is on the perpendicular bisector of that segment

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment

Let’s prove it!

Perpendicular Bisector Theorem

Proof of Perpendicular Bisector Theorem