Mastery Test Questions (10) 1. Question: What is the missing step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with DE AC. Prove: Proof: Statement Reason 1. DE AC Given 2. CAB EDB, ACB DEB If two lines are cut by a transversal, the corresponding angles are congruent. 3. ABC DBE AA criterion for similarity. 4.?? Corresponding side of similar triangles are proportional. 5. AB = AD + DB CB = CE + EB Segment Addition AD DB CE EB 6. Substitution Property of Equality 7. 1 1 Division 8. Subtraction Property of Equality Comment [s1]: It should be termed as intersected. Alt 1: Alt 2: Alt 3: Alt 4: AB AC DB DE AB DB CB EB AB CB ** AB AC CB DE
2. Question: The figure shows the blueprint for the construction of a section of an upcoming airport. If Route A and Route B shown in the blueprint are parallel, what will be the distance from Route A to Route B on Route C? Alt 1: 433 feet Alt 2: 975 feet** Alt 3: 1050 feet Alt 4: 1477 feet 3. Question: Lyra and Donna are testing the radio sets they built for their science project. Lyra gets on the roof of a building with one of the sets which is 22 meters high while Donna walks away from the building with the other set. When Donna goes beyond 50 meters from the building, the connection breaks. What is the approximate range of the radio sets? Alt 1: 45 meters Alt 2: 50 meters
Alt 3: 55 meters** Alt 4: 62 meters 4. Question: What is the third step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with m ABC = 90 Prove: AB 2 + BC 2 = AC 2 Proof: Statement Reason 1. Draw BD AC construction 2. ABC BDC Angles with the same measure are congruent. 3. Reflexive Property of Congruence 4. ABC BDC AA criterion of similarity BC AC Corresponding sides of similar triangles are 5. DC BC proportional. 6. BC 2 = AC DC cross multiplication 7. ABC ADB Angles with the same measure are congruent. 8. Reflexive Property of Congruence 9. ABC ADB AA criterion of similarity AB AC Corresponding sides of similar triangles are 10. AD AB proportional. 11. AB 2 = AC AD Cross Multiplication 12. AB 2 + BC 2 = AC AD + AC DC Addition 13. AB 2 + BC 2 = AC (AD + DC) Distributive Property 14. AB 2 + BC 2 = AC AC Segment Addition 15. AB 2 + BC 2 = AC 2 Multiplication Alt 1: BDC ADB Alt 2: BCA BCD** Alt 3: BAC BAD
Alt 4: DBC BAC 5. Question: Which of the figures show DE BC? Alt 1: Alt 2: Alt 3:
Alt 4: ** 6. Question: What is the missing step in the following proof? <Given, To Prove, and Proof will go in passage / image area> Given: ABC with Prove: DE AC. Proof:
Statement 1. Given 2.???? Reason AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6. ABC DBE Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8. BAC BDE congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s2]: This should be termed as intersected. Alt 1: Statement : DB EB Reason: Corresponding sides of congruent triangles are congruent. Alt 2: Statement: DE DE Reason: Addition Property of Equality Alt 3: Statement: 1 1** Reason: Addition Property of Equality Alt 4: Statement: AD EB CE DB Reason: Cross Multiplication 7. Question: Which of the following is true if AD AE? DB EC
Alt 1: Alt 2: Alt 3: DE FG DE BC ** FG BC Alt 4: DE FG BC 8. Question: Which of the following statements will be always true if BD is the altitude for right triangle ABC? Alt 1: ADB BDC Alt 2: ADB ~ BDC ** AB AC Alt 3: BC BD Alt 4: BAC BDC 9. Question: A pillar needs two beams to support its weight. Based on the diagram, at what height should the short beam connect the pillar to ensure that it's parallel to the long beam?
25 feet? 6 feet 9 feet Alt 1: 6 feet Alt 2: 10 feet** Alt 3: 12 feet Alt 4: 15 feet 10 Question: A group of boys are setting up a tent for their camp. The tent needs to be 12 feet high and 16 feet wide. What should be the minimum length of the sticks that the boys should use to setup the walls for the tent? Alt 1: 8 feet Alt 2: 13 feet Alt 3: 15 feet** Alt 4: 18 feet Pre-test Questions (4) 1. Question: What is the missing step in the following proof? Given: ABC with DE AC.
Prove: Proof: Statement Reason 1. DE AC Given 2.?? If two lines are cut by a transversal, the corresponding angles are congruent. 3. ABC DBE AA criterion for similarity. AB CB Corresponding side of similar triangles are 4. proportional. 5. AB = AD + DB CB = CE + EB Segment Addition AD DB CE EB 6. Substitution Property of Equality 7. 1 1 Division 8. Subtraction Property of Equality Comment [s3]: Should be termed as intersected. Alt 1: CAB ACB, EDB DEB Alt 2: ADE DBE, CED EBD Alt 3: CAD ACE, ADE CED Alt 4: CAB EDB, ACB DEB** 2. Question: The image shows the cable length for a cable car rail from point A to B and the ground distance between the two points. What will be the cable length from point B to C? Alt 1: 29 feet
Alt 2: 48 feet Alt 3: 56 feet** Alt 4: 60 feet 3. Question: What is the second step in the following proof? Given: ABC with m ABC = 90 Prove: AB 2 + BC 2 = AC 2 Proof: Statement Reason 1. Draw BD AC construction 2. Angles with the same measure are congruent. 3. BCA BCD Reflexive Property of Congruence 4. ABC BDC AA criterion of similarity BC AC Corresponding sides of similar triangles are 5. DC BC proportional. 6. BC 2 = AC DC cross multiplication 7. Angles with the same measure are congruent. 8. BAC BAD Reflexive Property of Congruence 9. ABC ABD AA criterion of similarity AB AC Corresponding sides of similar triangles are 10. AD AB proportional. 11. AB 2 = AC AD Cross Multiplication 12. AB 2 + BC 2 = AC AD + AC DC Addition 13. AB 2 + BC 2 = AC (AD + DC) Distributive Property 14. AB 2 + BC 2 = AC AC Segment Addition 15. AB 2 + BC 2 = AC 2 Multiplication Comment [s4]: It should be written as ADB. Alt 1: ABC BDC** Alt 2: ADB BDC Alt 3: ABC ADB
Alt 4: DBC BAC 4. Question: Which of the following ratios are true if FG BC in this figure? AD AE Alt 1: DF EG DF EG Alt 2: FB GC AD AE Alt 3: DB EC AF AG Alt 4: ** FB GC Unit Post-test Questions (4) 1. Question: What is the missing step in the following proof? Given: ABC with. Prove: DE AC
Proof: Statement Reason 1. Given 2. 1 1 Addition Property of Equality AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6.?? Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8. BAC BDE congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s5]: Should be termed as intersected. Alt 1: ABC DBE** Alt 2: BAC BDE Alt 3: ACB DEB Alt 4: BDE ADE Alt 5: CAB DAC 2. Question: A small plane takes off from point A and continues to climb upward in a straight line. The image shows its exact distance from and the ground distance from point A at different points during the take off. What will be its distance from the takeoff point when it's at point C??? B 56 feet A 52 feet 65 feet Alt 1: 70 feet Alt 2: 76 feet
Alt 3: 101 feet Alt 4: 126 feet** Alt 5: 134 feet 3. Question: Given a right triangle ABC, what construction do you need to perform while proving the Pythagoras theorem? Alt 1: Alt 2: Alt 3: **
Alt 4: Alt 5: 4. Question: Which of the following ratios are true if ADE ABC?
AD AE Alt 1: ** DB EC AF AG Alt 2: FB GC AD AE Alt 3: DF EG DF EG Alt 4: FB GC AD AE Alt 5: FB GC End-of-Semester Test Questions (2) 1. Question: What is the missing step in the following proof? Given: ABC with. Prove: DE AC Proof: Statement 1. Given Reason
2. 1 1 Addition Property of Equality AD DB CE EB 3. Using Common Denominators 4. AB = AD + DB CB = CE + EB Segment Addition AB CB 5. Substitution Property of Equality 6. ABC DBE Reflexive Property of Congruence 7. ABC DBE Side-Angle-Side Similarity Theorem Corresponding angles of similar triangles are 8.?? congruent. If the corresponding angles formed by two lines 9. DE AC cut by a transversal are congruent, then the lines are parallel. Comment [s6]: Should be termed as intersected. Alt 1: BAC ACB Alt 2: BDE DEB Alt 3: ADE DEC Alt 4: BAC BDE** Alt 5: ABC DBE 2. Question: A flight of stairs is supported by two pillars as shown. What is the distance of the second pillar from the bottom of the stairs? 12 feet 6 feet Alt 1: 6 feet Alt 2: 8 feet Alt 3: 12 feet** 4 feet??
Alt 4: 16 feet Alt 5: 20 feet