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Unit 1B2 Day 1 Do now Fill in the blank: If there is a line l and a point P not on l, then __________________________ through P, parallel to l. (Hint: It’s in your packet.) Classifying Triangles A triangle is a figure formed by _________ segments joining three ___________________ points. Classifying by sides Equilateral Isosceles Scalene Classifying by angles Acute Equiangular Right Obtuse Note An equilateral triangle is also acute. A triangle is equilateral if and only if it is equiangular. Classifying Triangles Ex. 1: Classify the following triangles both by sides and by angles. Ex. 1A Ex. 1a: Classify the triangle by sides and by angles. More Vocab. Each of the three points joining the sides of a triangle is a _____________ (plural: ______________). Two sides that share a vertex are ___________________. The third side is considered _______________ that vertex. More Vocab. In a right triangle, the sides that form the right angle are the _________. The side opposite the right angle is the ______________. In an isosceles triangle with exactly two congruent sides, the two congruent sides are called the ________. The remaining side is called the ___________. Ex. 2: Identifying Parts Classify the triangle both by sides and angles. Name the sides (hypotenuse, legs, base). Ex. 2A Ex. 2a: The diagram shows a bridge. Classify triangle MNO by sides and angles. Name the sides of triangle MNO. Using Angle Measures If you extend the sides of triangles, other angles are formed. Exterior angles Interior angles Triangle Sum Theorem (4.1) The sum of the measure of the interior angles of a triangle is _______. Do Now Complete the sentence with always, sometimes, or never. a) An isosceles triangle is ______ a right triangle. b) An obtuse triangle is ______ a right triangle. c) A right triangle is ______ an equilateral triangle. d) A right triangle is ______ an isosceles triangle. e) An equilateral triangle is _______ an acute triangle. Exterior Angle Theorem (4.2) The measure of an exterior angle of a triangle is equal to the sum of the measure of the two nonadjacent interior angles. Ex. 3: Finding an Angle Measure Find the value of x. Then find the measure of the of the exterior angle shown. Ex. 3A Ex. 3a: Find the value of x. Then find the measure of the given exterior angle. Corollary to the Triangle Sum Theorem A corollary to a theorem is a statement that follows easily from the theorem. Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are _____________. Ex. 4: Finding Angle Measures In a certain right triangle, the measure of one acute angle is two times the measure of the other. Find the measure of both angles. Ex. 4A The measure of one acute angle of a right triangle is one-fourth the measure of the other acute angle. Find the measure of both angles. Ex. 5 Find the measures of the numbered angles. Closure Can a scalene triangle be equiangular? Can an isosceles triangle be obtuse? Can a right triangle be equilateral?