Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW 1 Sketch and label an example of each statement a HG b A B c ST UV d M is the midpoint of PQ e Angles 1 and 2 are vertical angles f Angle C is a right angle 1
2 Sketch and label an example of each statement a HI JK b Angle R is acute c D E d d Angle 4 and 5 are vertical angles e e W is the midpoint of VX f f FG 2
3 Sketch and label each of the following geometric figures a Adjacent complementary angles ABC and CBD b Two intersecting lines with vertical angles 1 and 2 and vertical angles 3 and 4 c Name all of the linear pairs in the figure from part (b) d Name the congruent angles and the supplementary angles in the figure from part (b) 4 What is an angle bisector? Use a complete sentence in your answer 5 What does it mean when a line segment is bisected? Use a complete sentence in your answer 6 6 State the Segment Addition Postulate Write it as an If If and then then statement 3
7 Consider the conditional statement: If EG bisects DEF, then m DEG = m GEF a What is the hypothesis? Use a complete sentence in your answer b What is the conclusion? Use a complete sentence in your answer c What is the truth value of a conditional statement if p is true and q is false? Use a complete sentence in your answer 8 Consider the following statement: If M is the midpoint of AB, then AB = 2AM a What is the hypothesis? Use a complete sentence in your answer b What is the conclusion? Use a complete sentence in your answer c What is the truth value of the conditional statement if p is false and q is false? Explain Use a complete sentence in your answer 4
9 Construct an angle that is one fourth the measure of X 10 Construct the angle bisector of A 11 11 Construct a line perpendicular to AB through point C 5
12 A complement of an angle measures 10 degrees more than the measure of the angle What is the measure of the angle and its complement? Show all your work REMEMBER: YOU MUST STUDY THE VOCABULARY FROM THE CONCEPT PACKET PROVIDED TO YOU WHEN WE STARTED CH 1 YOU WILL BE TESTED ON THE VOCABULARY AS WELL 6
13 Create a two-column proof Given: m ABE = m DBC Prove: ABD EBC Statements Reasons 1 m ABE = m DBC 2 m ABD = m ABE + m EBD 3 m ABD = m DBC + m EBD 4 m EBC = m DBC + m EBD 5 ABD = EBC 6 ABD EBC Define each reason before using it in the two-column proof above: Given- Substitution Property- Transitive Property- Angle Addition Postulate- Definition of congruent angles- 7
14 Create a two-column proof Given: MN = OP Prove: MO NP Statements Reasons 1 MN = OP 2 MO = MN + NO 3 MO = NO + OP 4 NP = NO + OP 5 MO = NP 6 MO NP Define each reason before using it in the two-column proof above: Given- Substitution Property- Transitive Property- Segment Addition Postulate- Definition of congruent segments- 8
15 Write a two column proof for the following theorem Given: GBC = HEF ABG = DEH Prove: ABC = DEF Statements Reasons 1 GBC = HEF 2 ABG = DEH 3 GBC + ABG = HEF + DEH 4 GBC + ABG = ABC 5 HEF + DEH = DEF 6 ABC = DEF Define each reason before using it in the two-column proof above: Given- Angle Addition Property- Substitution Property- Addition Property of Equality- 9
ID: A CH 1 TEST REVIEW Answer Section 1 ANS: a b c d e f PTS: 1 REF: Ch12 TOP: End Ch Test 1
ID: A 2 ANS: a b c d e f PTS: 1 REF: Ch14 TOP: End Ch Test 2
ID: A 3 ANS: a b c The linear pairs are 1 and 3, 1 and 4, 2 and 3, and 2 and 4 d Angle pairs 1 and 2, and 3 and 4 are congruent Angle pairs 1 and 3, 1 and 4, 2 and 3, and 2 and 4 are supplementary PTS: 1 REF: Ch13 TOP: Standard Test 4 ANS: An angle bisector is a ray drawn through the vertex of an angle that divides it into two angles of equal measure PTS: 1 REF: Ch13 TOP: End Ch Test 5 ANS: A bisected line segment has been divided into two equal-length line segments or two congruent line segments PTS: 1 REF: Ch15 TOP: End Ch Test 6 ANS: If point B is on AC and between points A and C, then AB + BC = AC PTS: 1 REF: Ch12 TOP: Standard Test 3
ID: A 7 ANS: a a EG bisects DEF b m DEG = m GEF c The truth value of a conditional statement is false if p is true and q is false PTS: 1 REF: Ch12 TOP: Standard Test 8 ANS: a a M is the midpoint of AB b AB = 2AM c The truth value of the conditional statement is true By definition, a midpoint divides a segment into two congruent pieces If M is not the midpoint, then AB is not equal to 2AM PTS: 1 REF: Ch16 TOP: Standard Test 9 ANS: PTS: 1 REF: Ch12 TOP: End Ch Test 10 ANS: PTS: 1 REF: Ch15 TOP: Standard Test 4
ID: A 11 ANS: PTS: 1 REF: Ch11 TOP: Standard Test 12 ANS: x + (x + 10) = 90 2x = 80 x = 40 x + 10 = 50 40 + 50 = 90 The measure of the angle is 40 The measure of the complement is 50 PTS: 1 REF: Ch16 TOP: Standard Test 13 ANS: Statements Reasons 1 m ABE = m DBC 1 Given 2 m ABD = m ABE + m EBD 2 Angle Addition Postulate 3 m ABD = m DBC + m EBD 3 Substitution Property 4 m EBC = m DBC + m EBD 4 Angle Addition Postulate 5 ABD = EBC 5 Transitive Property 6 ABD EBC 6 Definition of congruent angles PTS: 1 REF: Ch11 TOP: Standard Test 5
ID: A 14 ANS: Statements Reasons 1 MN = OP 1 Given 2 MO = MN + NO 2 Segment Addition Postulate 3 MO = NO + OP 3 Substitution Property 4 NP = NO + OP 4 Segment Addition Postulate 5 MO = NP 5 Transitive Property 6 MO NP 6 Definition of congruent segments PTS: 1 REF: Ch13 TOP: End Ch Test 15 ANS: Statements Reasons 1 GBC = HEF 1 Given 2 ABG = DEH 2 Given 3 GBC + ABG = HEF + DEH 3 Addition Property of Equality 4 GBC + ABG = ABC 4 Angle Addition Property 5 HEF + DEH = DEF 5 Angle Addition Property 6 ABC = DEF 6 Substitution Property PTS: 1 REF: Ch13 TOP: Standard Test 6