Triangle Theorems

Warm Up Are the two triangles congruent? State why or why not. 1. 2. 10 minutes End

Warm Up 1. 2. Are the two triangles congruent? State why or why not. 1. 2. Assumption: Vertical Angles The triangles are congruent by ASA. Assumption: Reflexive Property The triangles are congruent by ASA.

Today’s Objective Students will explore three triangle theorems Triangle Angle Sum Theorem Midsegment Theorem Isosceles Triangle Theorem Give each person a triangle foldable. Have them write Triangle Thms on the front cover. Each thm should be recorded from today’s lesson

Explore this thm as a class Explore this thm as a class. Give each student a paper triangle and have them number the angles 1 2 and 3 (or a b and c). One by one, tear of the angles. Then lay the angles flat to form a line. Students should see that all their triangles’s angles summed to 180. Record in notes.

Examples Find the value of the missing angle: 2. 1. 3.

Group Work As a group, you will explore the remaining two theorems. Resource Manager: Choose a station to start on and pick up one worksheet for each person Time Keeper: Set the timer for 15 minutes (for each station) Reader: Read each question out loud Spy Monitor: Check in with others or the key After you finish a station, start on the next one Compare, make a conjecture, equiangular

Midsegments of Triangles Definition: The midsegment of a triangle is the segment connecting the midpoints of two sides of a triangle Midpoint Midpoint

Midsegment Theorem The midsegment is parallel to and half the distance of the base (the side it does not touch)

Ex. 3 Find x:

Isosceles Triangles Definition: Isosceles Triangles are triangles in which two or more sides are congruent

Isosceles Triangle Theorem and its Converse Two sides of a triangle are congruent if and only if the angles opposite those sides are congruent. So the legs must be congruent as well. These angles are congruent.

Examples

If m<A=4x+2 and m<C=2x+20, Find x.

Homework Worksheet