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Mathematician: _________________________ Date: _______________ Core-Geometry: 4.1 Triangle Sum and 4.2 Congruence and Triangles Warm-up: 1. Determine the distance between (10, 50) and (40, 90). 2. Determine the slope between (-8, -3) and (-12, -15). Constructions Review 1. Copy the given angle. 2. If the provided angle has x degrees, construct another angle that has ½x degrees. 1 4.1 Applying Triangle Sum Properties A ______________ is a polygon with three sides. A ________________with vertices A, B, and C is called _________________ _______ or using symbols ____ ______. Triangles can be classified by their _______________. No congruent sides At least 2 congruent sides 3 congruent sides Triangles may also be classified by their ______________. 3 acute angles 1 right angle 1 obtuse angle 3 congruent angles Note: An equilateral triangle can also be classified as ___________________. Example 1 Classify the triangles by sides and angles: 2 When the sides of a _______________ are extended, other angles are formed. The __________ angles are the _______________ angles. The angles formed by extending the lines form _______________ pairs. These angles are called __________________ angles. The Triangle ___________Theorem: The ________ of the measures of the ______________ angles of a triangle is _____________. Using what we know about linear pairs, we can find an important property for the measure of an exterior angle. The measure of an __________________ angle of a triangle is ____________ to the _____ of the measures of the two ____________________ _________________ angles. Example 2 Write equations and solve to find the variables below. Then find the measure of each missing angle. 3 4.2 Applying Congruence and Triangles Two __________________figures are congruent if they have _______________the same ___________ and ____________________. In two ____________________figures, all the _____________of one figure are _________________to the __________________________ parts of the other _______________. When you write a congruence statement for two polygons, it is important to list the corresponding _______________ is the same __________. What congruence statements can be written for the triangles below? Example 1 Find the value of the variable if Polygon ABCDE @ Polygon FGHIJ Example 2 Can you tell if the triangles below are congruent? Why? If they are congruent, write congruence statements for the triangles and all of the corresponding parts. 4 Third Angles: Using what you know about the sum of angle measures, what do you notice about the missing angles in the two triangles below? If two angles of one triangle are __________________ to two angles of another triangle, then the third angles are also ___________________. Example 3 Find the value of x. (a) (b) Hmwk 3.1 p.228 Ex 4.2 # 5-10, 11, 13, 15, 19, 21 p.221 Ex 4.1 # 1-6, 11, 15, 17, 19, 21-26, 27, 31, 33 5