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Transcript
Welcome Back!!! Get a new warmup sheet from front table and start this WARMUP Solve each equation. 1. x + 6 = 25 2. x + 7 + 13 = 33 3. 5x = 540 4. x + 10 = 2x 5. For the triangle below, use the Triangle Angle-Sum Theorem to find the value of y. Chapter 4: Congruent Triangles Objectives: To prove triangles are congruent given information about their sides and angles. Use congruent triangles to solve reallife problems. REVIEW: Triangles and Angles Objectives: Classify triangles by their sides and angles Find angle measures in triangles. Triangles: figure formed by 3 segments joining 3 noncollinear points. CLASSIFICATION BY SIDES (# of congruent sides) Scalene Triangle-no congruent sides Isosceles Triangle-at least 2 congruent sides Equilateral Triangle-3 congruent sides CLASSIFICATION BY ANGLES (all triangles have at least two acute angles, the third angle is used to classify) EQUIANGULAR TRIANGLE – 3 congruent sides (also acute) • Vertex – each of the three points joining the sides of a triangle. • Adjacent sides – two sides sharing a common vertex. • Opposite side – the third side not sharing the vertex Definitions: B B A C Interior angles – angles inside the triangle A Exterior angles – angles that are adjacent to the interior angles. C Theorem: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. mA mB mC 180 Theorem : Exterior Angle Theorem 1 The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m1 mA mB Checkpoint? 1. 110° (4x-7)° x° 2. The measure of one acute angle of a right triangle is five times the measure of the other acute angle. Find the measure of each acute angle. 4.1 Congruent Figures Objectives: Identify congruent figures and corresponding parts. Congruent figures – have exactly the same size and shape *Corresponding angles and sides are congruent. *3 ways to move a figure on top of another -Flip -Slide -Turn ******The order that the letters come in always display the corresponding relationship. Congruent Figures ABC QTJ. List the congruent corresponding parts. List the corresponding vertices in the same order. Angles: A Q B T C J List the corresponding sides in the same order. Sides: AB QT BC TJ AC QJ Checkpoint? In the diagram, ABCD KJHL , find: Find the value of x. A 9 91° B L (5y-12)° 86° D 6 113° C K 4x-3 H J Theorem 4.1: Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If A D and B F then C E Checkpoint? G K (4x-9)° F J 100° 45° H I Find the value of x. Congruent Figures Can you conclude that the figure below? ABC List corresponding vertices in the same order. If ABC CDE, then BAC DCE. The diagram above shows BAC DEC, not DCE. Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABC CDE. CDE in E H 58° G 58° F J Decide whether the triangles are congruent. Homework Pages 182-184 # 1-23, 24-27, 30-35, 38-40