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Studying Guide Carmeno and Ariana Table of Contents • 4.1: Classifying Triangles • 4.5:Proving Congruence • 4.2:Angles of Triangles • 4.6: Isosceles Triangles • 4.3: Congruent Triangles • 5.1: Bisector, Medians, and Altitudes • 4.4:Proving Congruence • Conclusion 4.5: Proving Congruence G H Line GK is congruent to line HJ. Line GH is congruent to line JK. K J X W SAS (Side . Angle . Side): Two sides and the included angle of one triangle are congruent to two sides and the included angles of the other triangle. Y Z SAS (Side . Angle . Side): Two sides and the included angle of one triangle are congruent to two sides and the included angles of the other triangle. Line WX is congruent to line YZ. Angle X is congruent to angle Z. Line WZ is most likely congruent to line XY. 4.6: Bisectors, Medians, and Altitudes G 6x - 5 X 5x J H 60° 3x + 8 Z Y 4x - 4 6x – 5 = 5x -6x -6x -5 = -1x -1 -1 5=X 3x + 8 = 4x – 4 +4 +4 3x + 12 = 4x - 3x -3x 12 = X 5.1 Bisectors, Medians, and Altitudes Find x if line AD is an altitude of triangle ABC. 2x – 15 = x + 7 What I did was I added 15 to both sides that way I’m left with 2x on one side and x + 22 on the other side. I then subtracted the x from x+22, and my final product was x = 22. I then plugged 22 into the equation for line AD and got 82°. Find x if line PS is median of triangle PQR. 10x – 7 = 5x + 3 What I did was add 7 to both sides that way I am left with the equation 10x = 5x + 10. I then subtracted 5x from the right side of the equal sign and I ended up with 5x = 10. I then had to divide by 5; I was left with x = 2. I plugged 2 into the x value of the equation 15x + 42. When you simplify the equation you should then have: 30 + 42; 72° is the final answer. Conclusion Three main messages to take from this chapter. • A few things that are important about this chapter might be learning what Isosceles, scalene, and equilateral triangles are, and how they differ from each other. Also, finding how a triangle is congruent and what sides and angles are congruent might be an important part about this chapter. Methods to find out how a triangle is congruent is also very helpful in this study guide. All corresponding parts of one triangle are congruent to the corresponding parts of the other triangle; as long as you know this then you would know how to tell whether a triangle is congruent or not. This chapter is full of helpful information to help identify triangles and their angles.