Geometry Topic 2 Lines, Angles, and Triangles
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1 Geometry Topic 2 Lines, Angles, and Triangles
2 MAFS.912.G-CO.3.9 Using the figure below and the fact that line is parallel to segment prove that the sum of the angle measurements in a triangle is 180. Sample answer: is parallel to segment 4 1and 5 3are alternate interior angles =180, definition of straight angle =180, substitution property of equality Therefore the sum of the angle measurement of the triangle is 180.
3 MAFS.912.G-CO.3.9 Using the figure below, prove that vertical angles are congruent. Sample answer: 4+ 1=180, linear pair 1+ 2=180, linear pair 4+ 1= 1+ 2, substitution property of equality Therefore, 4= 2.
4 MAFS.912.G-CO.2.8 Triangle and triangle are shown in the coordinate plane below. Part A: Explain why triangle is congruent to triangle using one or more reflections, rotations, and translations. Sample answer: a. Rotation of 180 about origin maps to. Part B: Explain how you can use the transformations described in Part A to prove triangle is congruent to triangle by any of the criteria for triangle congruence (ASA, SAS, or SSS). Sample answer: Rotation is a rigid transformation, which preserves side lengths and angle measurements. Therefore, SSS can be used.
5 MAFS.912.G-CO.3.10 In the figure below, bisects, =, =90, and =42. Find the measure of. =16
6 MAFS.912.G-CO.3.10 In the figure below, is the angle bisector of. and are straight lines, and. Prove that Sample answer: Statements angle bisector of and are straight lines Reasons Given Given Given Alternate interior angles are congruent Corresponding angles are congruent Definition of angle bisector Substitution property of equality If two angles of a triangleare equal, the opposite sides of the angles are equal.
7 MAFS.912.G-CO.2.7 & MAFS.912.G-CO.2.8 and,in the figure below are such that,, and. A. Which criteria for triangle congruence (ASA, SAS, SSS) implies that? A. SAS or ASA B. Describe a sequence of rigid transformations that shows. B. Sample answer: rotation and translation
8 MAFS.912.G-CO.3.10 Given that, =2(3 10), and = +15 ; find the value of. 5
9 MAFS.912.G-CO.3.10 A billboard on level ground is supported by a brace, as shown in the accompanying diagram. The measure of angle A is 15 greater than twice the measure of angle B. Determine the measure of angle A and the measure of angle B. 65 and 25
10 MAFS.912.G-CO.2.8 Given is equilateral,, and, prove. Sample answer: Statements is equilateral Reasons Given Given Given Definitionof equilateral triangle Side-angle-side postulate
11 MAFS.912.G-CO.3.9 Line nintersects lines land m, forming the angles shown in the diagram below. Which value of x would prove? A. 2.5 B. 4.5 C D B
12 MAFS.912.G-CO.2.8 Given: C is the midpoint of., Prove: Sample answer: Statements C is midpoint of, ABC DCE A D Reasons Given Given Given Definition of midpoint Side-angle-side postulate Corresponding parts of congruent triangles are congruent, CPCTC
13 MAFS.912.G-CO.4.12 The picture to the right shows a construction of a line through a given point that is parallel to a given line. Which statement justifies why the constructed line is parallel to the given line? A. When two lines are each perpendicular to a third line, the lines are parallel. B. When two lines are each parallel to a third line, the lines are parallel. C. When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel. D. When two lines are intersected by a transversal and corresponding angles are congruent, the lines are parallel. D
14 MAFS.912.G-CO.2.7 What additional information is required in order to prove the two triangles are congruent using the provided justification? Use the set of choices in the box below. Select a side or angle and place it in the appropriate region. Only one side or angle can be placed in each region. ASA Postulate SAS Theorem ASA; ABC ABD SAS;
15 MAFS.912.G-SRT.2.5 Use the figure below, where point S is the midpoint of.therefore. You wish to prove In addition to, what two congruence statements are needed to prove this congruence by: A. SSS and B. SAS WSR UST and C. ASA W U and WSR UST D. AAS R T and W U OR R T and WSR UST
16 MAFS.912.G-SRT.2.5 Consuela wants to determine the length of a power line that will be stretched over a lake. She cannot walk through the lake. She was able to take some measurements, hoping to determine the length of the power line. Her measurements are shown to the right. Consuela believes that the length of the power line is 625 feet, but she s not sure how to explain this to her boss. Using what you know about triangle congruence, help Consuela by writing a paragraph proof to show why the length of the power line is 625 feet. Sample Answer: Student should label the vertices and intersection of the figure. Then use side-angle-side postulate to prove that the length of the powerline is 625 feet.
17 MAFS.912.G-CO.3.10 The lengths of two sides of a triangle are 2 and 3units, where >3.Which inequality represents all possible lengths,, for the third side of the triangle? A. +3< <3 3 B. 3< <3 +3 C. 3< <2 D. 2 < <3 3 A
18 MAFS.912.G-CO.3.10 Use this diagram to answer the following question. What is the measure of? A. 15 B. 60 C. 120 D. 175 B
19 MAFS.912.G-CO.3.10 Given: + Prove: <7 + > ( + 2) + ( + 3) > > > 2 1 > 7 < 7
20 MAFS.912.G-SRT.2.5 Consider the two triangles shown. Part A Write an inequality that shows the relationship between and. A. Part B Write an inequality that shows the relationship between and. B.
21 MAFS.912.G-CO.4.12 Lewis is inscribing a square in a circle. He is at this stage, select the option that best describes his next step: A. Connect point B and the arc with a straight edge. B. Use the arcs and the center A to form a perpendicular bisector. C. Using C as the center, draw an arc outside the circle. D. Ignore the arcs drawn and draw another on the circumference of the circle. B
22 MAFS.912.G-CO.3.10 Two right triangles must be congruent if A. an acute angle in each triangle is congruent. B. the lengths of the hypotenuses are equal. C. the corresponding legs are congruent. D. the areas are equal. C
23 MAFS.912.G-GPE.2.5 Create the equation of the perpendicular bisector of, ( 4,4)and (4,8)in slope intercept form. = 2 + 6
24 MAFS.912.G-GPE.2.5 Determine the equation of the line that is parallel to = 3 +2and goes through (1,5) in slope intercept form. = 3 + 8
25 MAFS.912.G-GPE.2.5 Is triangle, where (4,4), (5,1), ( 1, 1), a right triangle? If so, which angle is the right angle? Justify your answer. Sample answer: m RS = = = 3 m ST m RT 1
26 MAFS.912.G-GPE.2.5 Line contains points ( 4,2)and ( 2,9). Line contains points (, 1)and ( 1,1). Find the value of if the lines are parallel. = 11 5
27 MAFS.912.G-GPE.2.5 An equation of line is = 2. Which is an equation of the line that is perpendicular to line and passes through the point ( 4,0)? A. = +2 B. = +8 C. = 2 2 D. = 2 +8 D
28 MAFS.912.G-GPE.2.5 Use the three ordered pairs 1,0, (10,3), and (15,4). Which of the following statements CANNOT be true? A. There is a line through that is parallel to B. There is a line through that is perpendicular to C. There is a line through that is the same line as D. There is a line through that intersects C
29 MAFS.912.G-GPE.2.5 Which of the following is NOT an equation for a line perpendicular to = 1? A. = 3/2 1 B =5 C. 4 6 D. 2 = 3/2 +1 D
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