Warm-up 1. How many degrees are in a triangle?

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Chapter 4: Congruent Triangles Lesson 1: Classifying Triangles.

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Presentation transcript:

Warm-up 1. How many degrees are in a triangle? 2. Classify the different types of triangles By Angle Measures By Side Lengths

Triangle Sum Theorem: The sum of the measures of the angles of a triangle is 180°. m<DA + m<DB + m<DC = 180°. A C B

Classifying Triangles By Angle Measures Equiangular Acute Right Obtuse By Side Lengths Equilateral Isosceles Scalene

Example 1: Ex. 1 Find the m < Z m < Z = 65

Example 2: Ex. 2 In triangle ABC, <ACB is a right angle, and CD AB. Find the values of a, b, and c. a = 70° b = 20° c = 20°

Example 3: Classify the triangles by their angles and sides Right Isosceles Obtuse Scalene

Corresponding Parts The matching parts of two figures.

Congruent Triangles Triangles (actually ALL geometric figures) that are the same ___________ and ___________ are ___________. Each triangle has ______ sides and ________ angles. If all _____ of the _______________ parts are ___________ then the triangles are ___________.

Midsegment A midsegment of a triangle is a segment that connects the midpoints of 2 sides of the triangle. Every triangle has 3 midsegments.

Midsegment Theorem The segment connecting the midpoints of 2 sides of a triangle is parallel to the third side and is half as long as that side DE = ½ AC

Find the value of x x = 3 x = 4

KH = 14 GK = 22 ST = 40

Give it a try… X is the midpoint of MN, Y is the midpoint of NO, and Z is the midpoint of MO. a. Find XZ. XZ = 9 b. If XY = 10, find MO. MO = 20

In triangle ACE, B is the midpoint of AC and D is the midpoint of CE. Find the value of x if a. AB = 4x – 5 and AC = 3x + 15 b. CD = 6x – 4 and DE = 4x + 8