Geometry - Study Guide for Semester 1 Geometry Exam Key

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1 Name: Hour: Date: / / Geometry - Study Guide for Semester 1 Geometry Exam Key 1. Read the following statement below and then write the inverse, converse, and contrapositive. If Zach receives a Lego City set for his birthday, then he will be happy. Inverse: If Zach does not receive a Lego City set for his birthday, then he will not be happy. Converse: If Zach is happy, then he receives a Lego City set for his birthday. Contrapositive: If Zach is not happy, then he didn t receive a Lego City set for his birthday.. For the statement above, write either bi-conditional or give a counterexample. Not biconditional. The original statement may be true, but the converse is not. A possible counterexample could be that Zach could be happy if he received a neato peachy keen train set for his birthday.. Define inductive reasoning. Give an example. Inductive reasoning is drawing a conclusion based upon a series of examples. Given 1,,, you would conclude that the next number is 4 because of the pattern. 4. Define deductive reasoning. Give an example. Deductive reasoning is drawing a conclusion using known facts. An example would be that given x = 10, we would conclude that x = 5 because we know that we can divide both sides of an equation by the same thing (multiplicative property of equality). Define each of the following terms 5. Quadrilateral A quadrilateral is a closed, 4-sided, plane shape. 6. Parallelogram A parallelogram is a quadrilateral with pairs of parallel opposite sides. 7. Trapezoid A trapezoid is a quadrilateral with exactly 1 pair of parallel opposite sides. 8. Isosceles Trapezoid An isosceles trapezoid with congruent legs (the non-parallel sides). The base angles (opposite the legs) are also congruent. 9. Kite A quadrilateral with pairs of congruent adjacent sides. 10. Rectangle A parallelogram with 1 right angle. 11. Rhombus A parallelogram with 1 pair of congruent adjacent sides. 1. Square A rhombus plus a rectangle.

2 1. Draw the flow chart for quadrilaterals using each of the terms for numbers What is the midpoint formula? Solve the midpoint of the points (5, ) and (8, ). x Midpoint = 1 + x, y 1 + y. The midpoint is ( 6.5, 0.5). 15. What is the distance formula? Solve the distance of the points (5, ) and (8, ). ( ) + ( y 1 y ). The distance between the two points is 4 = 5.80 D = x 1 x 16. How do you solve the hypotenuse of a triangle? Give an example when both legs of the triangle are equal to 8. To find the hypotenuse of a right triangle, you multiply the leg length by. The length of the hypotenuse in the example would be Supplementary angles equal how many degrees? Complementary angles equal how many degrees? Supplementary angles add to 180. Complementary angle add to cos( 150 ) = 1. sec( 10 ) = 19. sin90 =1 0. tan( 0 ) =. csc( 450 ) =1. cot( 0 ) =

3 For the shape at right, answer the following questions. J (, 4) K (4, 8) L (4, ) M (6, 7) 4. Find the slope and length of each side of the shape. Slope of JK =, length of JK = 0. Slope of KM = 1, length of KM = 5. Slope of ML =, length of ML = 0. Slope of JL = 1, length of JL = Find the slopes and midpoints of the diagonals KL and JM. Slope of KL = Undefined, midpoint KL = ( 4, 5.5). Slope of JM =, midpoint JM = ( 4, 5.5) What shape is shown above. The shape is a rectangle because both pairs of opposites are parallel (same slope) and congruent (same length) and because the adjacent sides meet a 90 angle (they have opposite reciprocal slopes). Use the shape below to answer the following questions. P (6, ) Q (, 5) R (6, 7) S (9, 5) 7. Find the slope and distance of each side of the shape. Slope QR =, distance QR = 1. Slope RS =, distance RS = 1. Slope SP =, distance SP = 1. Slope PQ =, distance PQ = Find the slopes and midpoints of the diagonals PR and QS. Slope PR is undefined, midpoint PR is 6, 5 ( ). Slope QS is 0, midpoint QS is ( 6, 5). 9. What shape is shown above. The shape is a rhombus. Both pairs of opposite sides are parallel (same slope) and all sides are congruent (same distance). 0. When the figure is reflected across the y-axis( r x=0 ), what are the coordinates of the resulting image? (, 7), (, 1), ( 6, ) ( ) ( x, y 7) or T, 7 1. When the figure is translated using the rule x, y ( ), what are the coordinates of the resulting image? ( 5, 0), ( 5, 6), ( 9, 5). When the figure is rotated 180 o, what are the coordinates of the resulting image? (, 7), (, 1), ( 6, ). When the figure is rotated 90 o clockwise, what are the coordinates of the resulting image? ( 7, ), ( 1, ), (, 6)

4 4. When the figure is dilated by a factor of, what are the coordinates of the resulting image? S (, 4) ( 6,1), S (, ) ( 6, 6), S (, 1) ( 6, ) 5. When the figure is reflected across the y-axis and then translated using the rule (x+8,y), what are the coordinates of the resulting image? r x=0 ( ) ( 10, 6), r x=0 ( ) ( 10,1), r x=0 ( ) ( 14, ) ( ), 6 ( ),1 ( ) 6, 6. What is the rule for the translation of ABC onto A B C? T ( 9, 8) or ( x, y) ( x + 9, y 8) 7. What type of rotation maps ABC onto A B C? R What type of rotation maps ABC onto A B C? R What is the equation of the line of reflection that maps ABC onto A B C? x =1 40. Graph the line x =. Find a second line of reflection so that the composite of the two reflections will translate Δ ABC 10 units to the right. Write the composite. x = 8, the composite is ( r x=8! r x= ) or T ( 10,0) 41. Reflect ABC over the line y = x and then over the line y = x ( r y= x! r y=x ). Fill in the table below. A (, ) B (1, 6) C (6, 10) A (, ) B ( 6,1) C ( 10, 6) A (, ) B ( 1, 6) C ( 6,10) What transformation results from this composite transformation? R Determine whether the problem below is done correctly or not. If not, identify any mistake(s) and correct it. Given: Line 1 Line A A A x x y y Reflect over 1 line then line ( point A) Distance between Line 1 and Line : x + y Distance between Point A and Point A : x + x + y + y - Should be y + x + y b/c the distance from line to A should be x + y Line 1 Line (x + y) Should be (x + y) x + y

5 4. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the type Rotation 44. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the type Dilation (with a negative scale factor) 45. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the type Reflection 46. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the A rotation and a reflection. 47. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the A rotation and a dilation. 48. For the problem below, the bold triangle, ABC, is transformed to its image. Identify the A rotation and a reflection.