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:
AD CE

DB EB
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.
AA criterion for similarity.
Corresponding side of similar triangles are
proportional.
3. ABC  DBE
4. ??
5. AB = AD + DB
CB = CE + EB
AD  DB CE  EB

DB
EB
AD
CE
7.
1
1
DB
EB
AD CE
8.

DB EB
6.
AB
DB
AB
Alt 2:
CB
AB
Alt 3:
DB
AB
Alt 4:
CB
Alt 1:
AC
DE
DB

EB
CB
**

EB
AC

DE

Segment Addition
Substitution Property of Equality
Division
Subtraction Property of Equality
Comment [s1]: It should be termed as
“intersected”.
** on correct alt
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
** on correct alt
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
** on correct alt
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: AB2 + BC2 = AC2
Proof:
Statement
Reason
1. Draw BD  AC
2. ABC  BDC
construction
3.
Reflexive Property of Congruence
4. ABC  BDC
BC AC
5.

DC BC
AA criterion of similarity
Corresponding sides of similar triangles are
proportional.
6. BC2 = AC × DC
cross multiplication
7. ABC  ADB
Angles with the same measure are congruent.
8.
9. ABC  ADB
Reflexive Property of Congruence
AA criterion of similarity
Corresponding sides of similar triangles are
proportional.
10.
AB AC

AD AB
11. AB2 = AC × AD
12. AB2 + BC2 = AC × AD + AC × DC
13. AB2 + BC2 = AC (AD + DC)
14. AB2 + BC2 = AC × AC
15. AB2 + BC2 = AC2
Alt 1: BDC  ADB
Alt 2: BCA  BCD**
Alt 3: BAC  BAD
Angles with the same measure are congruent.
Cross Multiplication
Addition
Distributive Property
Segment Addition
Multiplication
Alt 4: DBC  BAC
** on correct alt
5. Question: Which of the figures show DE || BC ?
Alt 1:
Alt 2:
Alt 3:
Alt 4:
**
** on correct alt
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:
AD CE
.

DB EB
Statement
Reason
AD CE
1.

DB EB
Given
2. ??
??
3.
AD  DB CE  EB

DB
EB
4. AB = AD + DB
CB = CE + EB
Using Common Denominators
Segment Addition
AB CB

DB EB
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
congruent.
If the corresponding angles formed by two lines
cut by a transversal are congruent, then the
lines are parallel.
5.
8. BAC  BDE
9. DE || AC
Alt 1:
Statement : DB  EB
Reason: Corresponding sides of congruent triangles are congruent.
Alt 2:
Statement:
AD
CE
 DE 
 DE
DB
EB
Reason: Addition Property of Equality
Alt 3:
Statement:
AD
CE
1
 1**
DB
EB
Reason: Addition Property of Equality
Statement: AD  EB  CE  DB
Reason: Cross Multiplication
** on correct alt
Alt 4:
7. Question: Which of the following is true if
AD AE
?

DB EC
Comment [s2]: This should be termed
as “intersected”.
Alt 1: DE || FG
Alt 2: DE || BC **
Alt 3: FG || BC
Alt 4: DE || FG || BC
** on correct alt
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

BC BD
Alt 4: BAC  BDC
Alt 3:
** on correct alt
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
** on correct alt
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
** on correct alt
Pre-test Questions (4)
1. Question: What is the missing step in the following proof?
Given: ABC with DE || AC .
Prove:
AD CE

DB EB
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.
4.
AB CB

DB EB
5. AB = AD + DB
CB = CE + EB
AD  DB CE  EB

DB
EB
AD
CE
7.
1
1
DB
EB
AD CE
8.

DB EB
6.
Corresponding side of similar triangles are
proportional.
Segment Addition
Substitution Property of Equality
Division
Subtraction Property of Equality
Alt 1: CAB  ACB, EDB  DEB
Alt 2: ADE  DBE, CED  EBD
Alt 3: CAD  ACE, ADE  CED
Alt 4: CAB  EDB, ACB  DEB**
** on correct alt
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
Comment [s3]: Should be termed as
“intersected”.
Alt 2: 48 feet
Alt 3: 56 feet**
Alt 4: 60 feet
** on correct alt
3. Question: What is the second step in the following proof?
Given: ABC with mABC = 90°
Prove: AB2 + BC2 = AC2
Proof:
Statement
Reason
1. Draw BD  AC
2.
construction
3. BCA  BCD
Reflexive Property of Congruence
4. ABC  BDC
BC AC
5.

DC BC
AA criterion of similarity
Corresponding sides of similar triangles are
proportional.
6. BC2 = AC × DC
cross multiplication
7.
Angles with the same measure are congruent.
8. BAC  BAD
9. ABC   ABD
AB AC
10.

AD AB
Reflexive Property of Congruence
AA criterion of similarity
Corresponding sides of similar triangles are
proportional.
11. AB2 = AC × AD
12. AB2 + BC2 = AC × AD + AC × DC
13. AB2 + BC2 = AC (AD + DC)
14. AB2 + BC2 = AC × AC
15. AB2 + BC2 = AC2
Cross Multiplication
Addition
Distributive Property
Segment Addition
Multiplication
Alt 1: ABC  BDC**
Alt 2: ADB  BDC
Alt 3: ABC  ADB
Angles with the same measure are congruent.
Comment [s4]: It should be written as
ADB.
Alt 4: DBC  BAC
** on correct alt
4. Question: Which of the following ratios are true if FG || BC in this figure?
AD
DF
DF
Alt 2:
FB
AD
Alt 3:
DB
AF
Alt 4:
FB
Alt 1:
AE
EG
EG

GC
AE

EC
AG
**

GC

** on correct alt
Unit Post-test Questions (4)
1. Question: What is the missing step in the following proof?
Given: ABC with
Prove: DE || AC
AD CE
.

DB EB
Proof:
Statement
Reason
AD CE
1.

DB EB
AD
CE
2.
1
1
DB
EB
AD  DB CE  EB
3.

DB
EB
Given
Addition Property of Equality
Using Common Denominators
4. AB = AD + DB
CB = CE + EB
5.
Segment Addition
AB CB

DB EB
Substitution Property of Equality
6. ??
Reflexive Property of Congruence
7. ABC  DBE
Side-Angle-Side Similarity Theorem
Corresponding angles of similar triangles are
congruent.
If the corresponding angles formed by two lines
cut by a transversal are congruent, then the
lines are parallel.
8. BAC  BDE
9. DE || AC
Alt 1: ABC  DBE**
Alt 2: BAC  BDE
Alt 3: ACB  DEB
Alt 4: BDE  ADE
Alt 5: CAB  DAC
** on correct alt
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
52 feet
Alt 1: 70 feet
Alt 2: 76 feet
A
65 feet
Comment [s5]: Should be termed as
“intersected”.
Alt 3: 101 feet
Alt 4: 126 feet**
Alt 5: 134 feet
** on correct alt
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:
** on correct alt
4. Question: Which of the following ratios are true if ADE  ABC ?
Alt 1:
Alt 2:
Alt 3:
Alt 4:
Alt 5:
AD
DB
AF
FB
AD
DF
DF
FB
AD
FB
AE
**
EC
AG

GC
AE

EG
EG

GC
AE

GC

** on correct alt
End-of-Semester Test Questions (2)
1. Question: What is the missing step in the following proof?
Given: ABC with
AD CE
.

DB EB
Prove: DE || AC
Proof:
Statement
AD CE
1.

DB EB
Reason
Given
AD
CE
1
1
DB
EB
AD  DB CE  EB
3.

DB
EB
2.
Addition Property of Equality
Using Common Denominators
4. AB = AD + DB
CB = CE + EB
Segment Addition
AB CB

DB EB
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
congruent.
If the corresponding angles formed by two lines
cut by a transversal are congruent, then the
lines are parallel.
5.
8. ??
9. DE || AC
Alt 1: BAC  ACB
Alt 2: BDE  DEB
Alt 3: ADE  DEC
Alt 4: BAC  BDE**
Alt 5: ABC  DBE
** on correct alt
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
4 feet
??
Alt 1: 6 feet
Alt 2: 8 feet
Alt 3: 12 feet**
Comment [s6]: Should be termed as
“intersected”.
Alt 4: 16 feet
Alt 5: 20 feet
** on correct alt