INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY

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1 INTUITIVE GEOMETRY SEMESTER EXM ITEM SPEIFITION SHEET & KEY onstructed Response # Objective Syllabus Objective NV State Standard istinguish among the properties of various quadrilaterals lassify triangles by angle or side measure onstruct geometric figures involving lines and angles Multiple hoice # Objective Syllabus Objective NV State Standard Practice Key lassify pairs of angles lassify pairs of angles Solve angle measure problems Formulate strategies for determining distance between two points Formulate strategies for determining distance between two points Formulate strategies for determining the midpoint of a segment Explore geometric or algebraic relationships using patterns ompare deductive and inductive arguments ompare deductive and inductive arguments Solve problems using postulates & theorems related to parallel and perpendicular lines Solve problems using postulates & theorems related to parallel and perpendicular lines Solve problems using postulates & theorems related to parallel and perpendicular lines Explore conditions which guarantee parallel and perpendicular lines justify conclusions to problems on parallel & perpendicular lines using postulates and theorems lassify triangles by angle or side measure Solve problems involving angles of a triangle Solve and prove problems using the theorems and postulates for congruence Solve and prove problems using the theorems and postulates for congruence Solve and prove problems using the theorems and postulates for congruence Solve and prove problems using corresponding parts of congruent triangles Solve and prove problems using corresponding parts of congruent triangles Solve problems involving angles of a triangle Recognize the relationship between sides and angles of a triangle Verify that three given sides form a triangle lassify polygons lassify polygons Final Key Page of Revised: 8/0/08 lark ounty School istrict

2 INTUITIVE GEOMETRY SEMESTER EXM ITEM SPEIFITION SHEET & KEY Multiple hoice # Objective Syllabus Objective 7 Solve problems involving the sum of interior angles of a given polygons. 8 Solve problems relating to properties of quadrilaterals using algebraic techniques. 9 evelop strategies for finding the measures of an interior angle of a given regular polygon. NV State Standard Practice Key Explore relationships within each quadrilateral istinguish among the properties of various quadrilaterals Solve problems relating to properties of quadrilaterals using algebraic techniques evelop strategies for finding the measures of an interior angle of a given regular polygon Recognize the relationship between sides and angles of a triangle Explore geometric or algebraic relationships using patterns ompose examples of deductive reasoning in real world situations Formulate strategies for determining the slope of a line istinguish among the properties of various quadrilaterals Explore relationships within each quadrilateral ompose examples of deductive reasoning in real world situations istinguish between a hypothesis and the conclusion of a conditional statement Identify parallel, perpendicular and intersecting lines using slope Identify parallel, perpendicular and intersecting lines using slope Propose a conclusion from given information istinguish among the various terms associated with an angle Justify conclusions to problems using the theorems related to angles Justify conclusions to problems using the theorems related to angles evelop accuracy using geometric tools istinguish among the median, altitude, angle bisector, and perpendicular bisector of a triangle istinguish among the median, altitude, angle bisector, and perpendicular bisector of a triangle Final Key Page of Revised: 8/0/08 lark ounty School istrict

3 . Use the figure below.. In the diagram below, m = ( 7x + ) Which best describes the pair of angles: 4 and 5? ( x ). vertical. adjacent. linear pair. complementary. In the diagram below, F, E, and E are right angles. E F 4 Which best describes the pair of angles: and 4?. vertical. adjacent. supplementary. complementary What is the value of x? In the figure below, Y is between X and Z and XZ = 40 cm X a + 8 What is the value of a? Y a Z GO ON

4 5. What is the distance between points, 6,? ( ) and ( ) ( ) ( ) d = x x + y y 6. What are the coordinates midpoint of the, 4 and.... segment joining the points ( ) ( 4, )? Midpoint: x + x, y + y,,,, 7. In the pattern below, the sides of each regular hexagon have a length of unit. 8. What type of reasoning is based on definitions, postulates, and theorems?. deductive. hypothetical. inductive. scientific 9. Which statement is the inverse of: If an angle is acute, then it is not obtuse?. If an angle is obtuse, then it is not acute.. If an angle is acute, then it is obtuse.. If an angle is not obtuse, then it is acute.. If an angle is not acute, then it is obtuse. 0. In the figure below line m is a transversal. Which best describes the pair of angles: and?. alternate exterior. alternate interior. corresponding. vertical m What is the perimeter of the. 8 units. units. 6 units. 0 units th 5 figure? GO ON

5 . In the figure below, n m and l is a transversal What is the value of x?. In the figure below, n m and l is a transversal n m m n 64 ( 4x 6) x What is the value of x? l 7 l. In the figure below, m FGH = l m What value of x would make line l parallel to line m? 4. In the figure below, lines l and m are parallel. l m 4 ( x 7) 7 8 Which statement is true considering the given information?. and are congruent.. and 8 are supplementary.. and 4 are supplementary.. 6 and 7 are congruent. G H F GO ON

6 5. Which is a valid classification for a triangle? 7. In the figures below, EF RSTUVW.. cute and right. Isosceles and scalene. Isosceles and right. Obtuse and equiangular 6. Use the triangle below. F x E 45 ( x + ) W R What is the value of x? V S U T Which side of RSTUVW corresponds to E?. RW. SR. UT. UV GO ON

7 8. Use the triangles below. 0. Given that ΔRST Δ XYZ, m R 7n m X = 8n, = ( + ), and ( ) what is the value of n? Which congruence postulate or theorem would prove that these two triangles are congruent?. angle-angle-side. angle-side-angle. side-angle-side. side-side-side. Given that ΔPQR Δ JKL, PQ = 4x +, JK = 44, KL = 4, and JL =, what is the value of x? In the isosceles triangle below, m H = In the diagram below, and. Which congruence postulate or theorem would prove that these two triangles are congruent?. angle-angle-angle. angle-side-angle. side-side-side. side-angle-side E F What is the measure of H F? G GO ON

8 . In Δ, is a right angle and m = 40. Which list shows the sides in order from longest to shortest?.,, 6. Which figure is a polygon?..,,.,,.,,. 4. triangle has two sides that have lengths of 7 cm and 7 cm. Which could represent the length of the third side of the triangle?. 4 cm. 8 cm. 0 cm. 7 cm 5. How many sides does a nonagon have? hexagon is shown below. a What is the value of a? GO ON

9 8. Parallelogram is given below.. Use the rhombus below (x + 6) What is the value of x? E What is the measure of each exterior angle of a regular hexagon? Which statement is true about a kite?. kite has 4 congruent sides.. kite has pairs of parallel sides.. kite has congruent diagonals.. kite has perpendicular diagonals.. Which statement below is true about an isosceles trapezoid?. oth pairs of opposite sides are parallel.. oth pairs of opposite sides are congruent.. One pair of opposite sides is congruent and the other is parallel.. One pair of opposite sides is both parallel and congruent. What is m E? What is the measure of one interior angle of a regular octagon? Given that Δ FGH is an isosceles right triangle, what is the measure of an acute angle of the triangle? GO ON

10 5. What is the 6 th term of the sequence,, 4, 8,? Geometric figures are displayed on a computer screen in the following order: triangle, concave quadrilateral, convex pentagon, concave hexagon. Using inductive reasoning, what prediction can be made about the next figure?. It will be a concave heptagon.. It will be a convex heptagon.. It will be a convex polygon, but the type cannot be predicted.. It will be a polygon, but no other details about it can be predicted. 7. What is the slope of the line through, 4 and 7,? points ( ) ( ) y y slope = x x What property below is true for both a rectangle and a rhombus?. iagonals bisect each other.. iagonals bisect the angles.. iagonals are congruent.. iagonals are perpendicular. 9. rectangle LWYS has which of the following properties?. iagonals are congruent.. iagonals are perpendicular.. Four congruent sides.. Only one pair of congruent sides. 40. If a run is scored in baseball, then a player has crossed home plate. This is an example of what kind of reasoning?. scientific. inductive. deductive. conclusion 4. In the conditional statement, If it is rainy, then it is cloudy, what is the underlined portion called?. conclusion. converse. inverse. hypothesis GO ON

11 4. han graphs a line with the equation y = x 7. What is the slope of a line parallel to han s line? line has a slope of. What is the slope of a line that is perpendicular to it? Using the following conditionals: If I do my homework, then I will pass the test. If I pass the test, then I will get my cell phone back. What conclusion can be logically deduced?. If I get my cell phone back, then I passed the test.. If I passed the test, then I did my homework.. If I get my cell phone back, then I will call my friend.. If I do my homework, then I will get my cell phone back. 45. Given the angle below:. Which term best describes in relation to?. angle bisector. exterior. side. vertex GO ON

12 46. Use the diagram below: 47. Use the diagram below: Which statement justifies the conclusion that m 5= m + m 4?. Exterior ngle Theorem. Linear Pair Theorem. Triangle Sum Theorem. Vertical ngle Theorem Which statement justifies the conclusion that m + m 5 = 80?. Exterior ngle Theorem. Linear Pair Theorem. Triangle Sum Theorem. Vertical ngle Theorem 48. Use the protractor pictured below. X Z What is the measure of XYZ? Y GO ON

13 49. Given Δ : E What type of special segment is E?. ltitude. ngle isector. Median. Perpendicular isector 50. Given Δ KML : K M L X What type of special segment is XL?. Perpendicular isector. Median. ngle isector. ltitude

15 Free Response. is a parallelogram with measures as noted. ompute the measures, in degrees, of all missing angles.. ( 4x ) (x 9) a e ( x + 0) ( x + 0) h b f g c d x = m = m = m = a = b = c = d = e = f = g = h = GO ON

16 Free Response. nswer each part below.. What are the different ways an angle can be classified?. Using your answer from Part, sketch an isosceles triangle with a vertex angle of each of the types listed in Part. If such a triangle cannot exist, explain why GO ON

17 Free Response. Use angle below to answer Part and Part.. Write a description, in paragraph form, of the steps used to construct an angle bisector of the angle.. o the construction

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex.

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex. Polygons Polygon A closed plane figure formed by 3 or more segments. Each segment intersects exactly 2 other segments at their endpoints. No 2 segments with a common endpoint are collinear. Note: Each