Ch 4 Notesheet Key

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Ch 4 Note Sheet L1 Key Name ___________________________ 4.1 Triangles Sum Conjectures These notes replace pages 200 – 202 in the book. See step 4 of the Investigation. Rigidity is a property that triangles have. They cannot be shifted, like a quadrilateral can. They retain their shape. Triangulation is a procedure used by surveyors to locate a position by using triangles. Triangle Sum Conjecture The sum of the measures of the angles in every triangle is 180°. Numeric Example: Find x. A 56 B 101 101 + 56 + x = 180 x = 180 – 157 = 23 x C Find y. x + x + y = 180 2x + y = 180 y = 180 – 2x E x F x y D Third Angle Conjecture If two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are congruent. Numeric Example: If m∠ K = m∠Band m∠ I = m∠ C , find y. Give reasons for your answer! K 101 B A y 56 23 J I C y = 56 because the third angles are equal also. See Ch 4 Worksheet to prove these conjectures. S. Stirling Page 2 of 15
Ch 4 Note Sheet L1 Key Name ___________________________ Lesson 4.2 Properties of Isosceles Triangles Read top of page 206. This vocabulary is review! Know it!! Remember! With If..then.. statements: If a, then b. The converse of the statement is If b, then a. Label and define the special vocabulary for the isosceles triangle Δ VBS . B A leg (of an isosceles triangle) is one of the congruent sides. VB and VS S The base (of an isosceles triangle) is the side that is not a leg. BS The vertex angle is the angle between the two legs. ∠ V V The base angles are the pair of angles whose vertices are the endpoints of the base. ∠B and ∠ S Do group Investigation 1, Base angles of an Isosceles Triangle on page 207. Isosceles Triangle Conjecture If a triangle is isosceles, then its base angles are congruent. Given If VB ΔVBS with VB = VS , then ∠B ≅∠ S or ≅ VS , then ∠B ≅ ∠ S . B V S ***Note: Since equilateral triangles are a special case of isosceles triangles, any property that applies to isosceles triangles also apply to equilateral triangles. Do group Investigation 2, Is the Converse True? on page 208. Use a protractor. Converse of the Isosceles Triangle Conjecture If a triangle has two congruent angles, then it is an isosceles triangle. If ∠B ≅ ∠ S , then ΔVBS is isosceles or If ∠B ≅ ∠ S , then VB ≅ VS . V B S S. Stirling Page 3 of 15
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Ch 4 Notesheet Key

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