4.01 Writing Assignment Introduction to Triangles - Geometry Writing Assignment \u2013 Introduction to Triangles Each problem is worth 5 points Total

4.01 Writing Assignment Introduction to Triangles -...

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Unformatted text preview: Geometry Writing Assignment – Introduction to Triangles Each problem is worth 5 points Total Points: 50 Solve the problems pertaining triangles. Be sure to show all work when needed. 1. Explain your reasoning. 2 RW = RU . Kendra disagrees. Is either of them correct? 3 Kendra is right for disagreeing since RU is bigger than RW therefore RU is bigger than (2/3)RW a. Based on the figure, Jordan says that b. If QW = 27 inches, find QT. QT = QW + WT QT = 27 + WT 2. Jordan says that from the information supplied in the diagram, she can conclude that R is on the perpendicular bisector of QS . Robert disagrees. Is either of them correct? Explain your reasoning. A perpendicular bisector is a perpendicular line drawn from the midpoint of a side and while it can cross the opposite vertex like in an isoceles or an equilateral triangle it would then be the altitude of the triangle. In this case based only in the drawing we can say that R is on the perpendicular bisector of QS but it isn't always the case that the oposite vertex of a side is on it's perpendicular bisector. 3. Franklin measured and labeled the angles of a triangle as shown. Jennifer says that at least one of his measures is incorrect. Explain in at least two different ways how Jennifer knows that this is true. The triangle sum theorem states that the sum of all the interior angles of a triangle is 180 therefore 97 + 37 + 134 = 268 A triangle cant have 2 angles of 90 degrees or more 4. Joey says that triangle XYZ is obtuse. Robin disagrees because there are more acute angles then there are obtuse angles therefore it must be acute. Is either one of them correct? Explain your reasoning. Joey is correct An obtuse triangle is defined by having atleast an angle bigger than 90 degrees and two acute angles. 5. Compare and contrast the perpendicular bisectors and angle bisectors of a triangle. How are they alike? How are they different? Perpendicular bisectors are drawn perpendicular from the midpoint of the side of a triangle and when drawn from all sides the point where they meet is called the circumcenter Angle bisector are drawn from the vertex of an angle creating two angles of the same measure and when drawn from all angles the point where they meet is called incenter 6. Compare and contrast the perpendicular bisectors, medians, and altitudes of a triangle. How are they alike? How are they different? the altitude of a triangle is drawn from one vertex and is perpendicular to the oposite side while the medias are drawn from a vertex to the midpoint of the oposite side. a perpendicular bisector is drawn perperndicular from the midpoint of the side of a triangle but not necessarily crosses the oposite vertex. 7a. Classify triangle ABC by its sides if side AB = 6x, side AC = 4x + 6 and side BC = 8x + 3. The perimeter of triangle ABC is 63. Show all your work. 6x + 4x + 6 + 8x +3 = 63 , 18x + 9 = 63 , 18x + 9 - 9 = 63 - 9 , 18x = 54 , 18x/18 = 54 /18 , x = 3 AB = 6(3) = 18 , AC = 4(3) + 6 = 18 , BC = 8(3) + 3 = 27. Since two sides are the same it's an isoceles b. Explain your reasoning. An isoceles is formed from 2 equal sides and a different one since AB = AC then ABC is an isoceles. 8. Is there enough information given to find the value of X. Explain your reasoning. There isn't enough information to find the value of X. We can find the angles of the other triangle using exterior angles theorem to and interior angles theorem to find the angles having angles of 90 degrees and 67 degrees but for the triangle where the x is found we know one angles measures 90 degrees from the exterior angles theorem but we lack information for the X and the other side. ...
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