4TH QUARTER REVIEWER

MATHEMATICS GRADE 9
SY 2022 – 2023
1. Which of the following statements is FALSE?
A. All equiangular triangles are similar.
B. All equilateral triangles are similar.
C. All Isosceles triangles are similar.
D. All isosceles right triangles are similar.
2. If the foot of a 13-meter ladder is placed 5 meters away from a building,
how high up the building will the ladder reach?
A. 7 meters B. 9 meters C. 11 meters D. 12 meters

3. A 45 0−450−90 0triangle is also known as ______________________.

A. Equilateral triangle B. Scalene Triangle C. Isosceles Right Triangle D. Rectangle
4. The sides of a triangle are 5, 10 and 15. The shortest side of a similar triangle is 10. What is the length of the
longest side of this similar triangle?
A. 5 B. 20 c. 30 D. 40
5. In an isosceles right triangle, the hypotenuse is _______ times as long as each leg.
√2
A. twice B. one half C. √2 D.
2
6. What is the geometric mean of 2 and 8?
A. 4 B. 6 C. √5 D. √6
7. It is an equality of two ratios.
A. Proportion B. scale factor C. extremes D. means

8. Given a proportion, 2 : x = 7 : 35, what is the value of x?

A. 10 B. 15 C. 20 D. 25
9. Two triangles are similar if all pairs of corresponding sides are ________________.
A. Congruent B. Proportional C. Similar D. Perpendicular

10. In a 45 ° −45 °−90 ° , if one of the legs is equal to 7, what is the length of the hypotenuse?
A. 7 B. 14 C.7 √ 3 D.7 √ 2
For items 11 – 13, refer to the figure below.
11. If b = 9 and c = 4, find h.
A. 6 B. 8 C. 10 D. 12

12. If b = 3 and h = 6, find c.

A. 10 B. 12 C. 14 D. 16

13. Which of the following can be the name of the hypotenuse of ∆ AD M ?

A. b+c B. g C. m D. h

14. Which of the following given can be the sides of a right triangle?
A. 6, 9, 13 B. 5, 12, 13 C. 5, 7, 9 D. 4, 4, 10

15. Similar triangles are triangles whose corresponding angles are _________ and corresponding sides are
_________.
A. congruent; congruent C. congruent, proportional
B. proportional; congruent D. proportional; proportional
For numbers 16 - 18, identify what theorem is being stated.
A. SSS Similarity Theorem C. Triangle Angle-Bisector Theorem
B. SAS Similarity Theorem D. AA Similarity Theorem
16. If a segment bisects an angle of a triangle, then it divides the opposite side into segments proportional to the
other two sides.

17. Two triangles are similar if the corresponding sides of two triangles are in proportion.

18. If the two angles of one triangle are congruent to corresponding two angles of another triangle, the two triangles
are similar.
19. Duke plans to divide an 80-meter stick into three pieces in the ratio 1: 2: 5. What will be the length of each piece?
A. 10 B. 15 C. 20 D. 50
20. What are means in the given a proportion, w : x = y : z?
A. w and x B. w and z C. x and y D. x and z
21. Which of the following is an example of a proportion?
A. 3 : 6 = 14 : 28 B. 4 : 10 = 2 : 15 C. 8 : 2 = 6 : 12 D. 10 : 11 = 14 : 15
22. Complete the statement, “ In a proportion, the ______ of the means is equal to the product of the extremes.
A. sum B. difference C. product D. quotient
23. The angles of a triangle are in the ratio 1:2:3. What kind of triangle is described?
a. Acute Triangle B. Right Triangle C. Obtuse Triangle D. Equiangular Triangle
a b
24. If a, b and c are positive numbers, and = , then b is called the ____________ of a and c. What word/s will
b c
best fit the statement?
A. congruent b. proportional c. geometric mean D. perpendicular
25. The ratio of the angles in a triangle measure is 1:1:2. What kind of triangle is described?
A. Scalene Triangle b. Isosceles Triangle c. Equilateral Triangle D. Equiangular Triangle
26. Which of the following statement is true?
A. A 45 ° −45 °−90 ° triangle is a scalene triangle.
B. The hypotenuse of an isosceles right triangle is √ 3 times the length of either of the two legs.
C. A 45 °−45 °−90 ° triangle was formed out of an equilateral triangle.
D. The legs of 45 ° −45 °−90 ° triangle are congruent.
For items 27 – 30, refer to the given ∆ SHR ∆ WIN .
27. Which of the following is NOT a pair of corresponding vertices?
A. S ↔W B. R↔ N C. H↔ N D. H ↔ I
28. Which of the following pair of angles are congruent?
A. LS≅ LN B. LH≅ LW C. LR≅ LI D. LS≅ LW
29. Which of the following proportions is correct?
SH HR SR HR HR SH SN WN
A. = B. = C. = D. =
WI ¿ WI RN WN ¿ RW HI
30. If SH = 3, HR = 5, and WI =6, what is the measure of IN?
A. 8 B. 9 C. 10 D. 11
31. In a 30°−60 °−90 °, if the shorter leg is equal to 5, what is the length of the longer leg?
A. 5√ 2 B. 5√ 3 C. 10 D. 5

32. What is the ratio of the 30°−60 °−90 °triangle in increasing order?
A. 1:√ 3 :2 B. 1:2 : √ 3 C. 1:2 : √ 2 D. 1:√ 2: 2
x
33. Refer to the figure at the right, how long is the measure of x?
A. 3√ 3 m. B. 6 m. C. 3m. D. 3√ 2m. 60°
D 3m.
34. Given ∆ YOU , find the value of x. O
A. 5√ 3 B. 3√ 5 C. 9√ 5 D. 15
x

Y 6 3
35. Use the figure at the right to solve for m. U
A. 3 B. 4 C. 5 D. 6 9 5

36. If a man walks 7km east and then 6 km south, how far is he from the point where he started? n
A. √ 42 km B. √ 37 km C. √ 41 km D. √ 51 km
37. Which of the following is NOT a proportion? 8 6
5 50 2 10 7 14 1 5
A. = B. = C. = D. =
6 60 10 50 14 28 10 25
m
m
38. What do we call to the uniform ratio k of the corresponding proportional sides of polygons?
A. Ratio B. Scale Factor C. Dilation D. Geometric mean
N
39. Given ∆ MEL ∆ BEN , what is the mL1 if measure of L2 is 65°? M
A. 25° B. 45° C. 65° D. 90° 1
2 E B
L

A
40. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. What theorem is
stated?
A. SAS Similarity Theorem B. TABT c. TPT D. Pythagorean Theorem

4TH QUARTER REVIEWER KEY ANSWER

MATHEMATICS GRADE 9
SY 2022 – 2023
1. Which of the following statements is FALSE?
A. All equiangular triangles are similar.
B. All equilateral triangles are similar.
C. All Isosceles triangles are similar.
D. All isosceles right triangles are similar.
2. If the foot of a 13-meter ladder is placed 5 meters away from a building,
how high up the building will the ladder reach?
A. 7 meters B. 9 meters C. 11 meters D. 12 meters

3. A 45 0−450−90 0triangle is also known as ______________________.

A. Equilateral triangle B. Scalene Triangle C. Isosceles Right Triangle D. Rectangle
4. The sides of a triangle are 5, 10 and 15. The shortest side of a similar triangle is 10. What is the length of the
longest side of this similar triangle?
A. 5 B. 20 c. 30 D. 40
5. In an isosceles right triangle, the hypotenuse is _______ times as long as each leg.
√2
A. twice B. one half C. √2 D.
2
6. What is the geometric mean of 2 and 8?
A. 4 B. 6 C. √5 D. √6
7. It is an equality of two ratios.
A. Proportion B. scale factor C. extremes D. means

8. Given a proportion, 2 : x = 7 : 35, what is the value of x?

A. 10 B. 15 C. 20 D. 25
9. Two triangles are similar if all pairs of corresponding sides are ________________.
A. Congruent B. Proportional C. Similar D. Perpendicular

10. In a 45 ° −45 °−90 ° , if one of the legs is equal to 7, what is the length of the hypotenuse?
A. 7 B. 14 C.7 √ 3 D.7 √ 2
For items 11 – 13, refer to the figure below.
11. If b = 9 and c = 4, find h.
A. 6 B. 8 C. 10 D. 12

12. If b = 3 and h = 6, find c.

A. 10 B. 12 C. 14 D. 16

13. Which of the following can be the name of the hypotenuse of ∆ ADM ?
A. b+c B. g C. m D. h

14. Which of the following given can be the sides of a right triangle?
A. 6, 9, 13 B. 5, 12, 13 C. 5, 7, 9 D. 4, 4, 10

15. Similar triangles are triangles whose corresponding angles are _________ and corresponding sides are
_________.
A. congruent; congruent C. congruent; proportional
B. proportional; congruent D. proportional; proportional
For numbers 16 - 18, identify what theorem is being stated.
A. SSS Similarity Theorem C. Triangle Angle-Bisector Theorem
B. SAS Similarity Theorem D. AA Similarity Theorem
16. If a segment bisects an angle of a triangle, then it divides the opposite side into segments proportional to the
other two sides. (C. Triangle Angle-Bisector Theorem)
17. Two triangles are similar if the corresponding sides of two triangles are in proportion. (A. SSS Similarity
Theorem)
18. If the two angles of one triangle are congruent to corresponding two angles of another triangle, the two triangles
are similar. (D. AA Similarity Theorem)
19. Duke plans to divide an 80-meter stick into three pieces in the ratio 1: 2: 5. What will be the length of the
shortest piece?
A. 10 B. 15 C. 20 D. 50
20. What are means in the given a proportion, w : x = y : z?
A. w and x B. w and z C. x and y D. x and z
21. Which of the following is an example of a proportion?
A. 3 : 6 = 14 : 28 B. 4 : 10 = 2 : 15 C. 8 : 2 = 6 : 12 D. 10 : 11 = 14 : 15
22. Complete the statement, “ In a proportion, the ______ of the means is equal to the product of the extremes.
A. sum B. difference C. product D. quotient
23. The angles of a triangle are in the ratio 1:2:3. What kind of triangle is described?
a. Acute Triangle B. Right Triangle C. Obtuse Triangle D. Equiangular Triangle
a b
24. If a, b and c are positive numbers, and = , then b is called the ____________ of a and c. What word/s will
b c
best fit the statement?
A. congruent b. proportional c. geometric mean D. perpendicular
25. The ratio of the angles in a triangle measure is 1:1:2. What kind of triangle is described?
A. Scalene Triangle b. Isosceles Triangle c. Equilateral Triangle D. Equiangular Triangle
26. Which of the following statement is true?
A. A 45 ° −45 °−90 ° triangle is a scalene triangle.
B. The hypotenuse of an isosceles right triangle is √ 3 times the length of either of the two legs.
C. A 45 °−45 °−90 ° triangle was formed out of an equilateral triangle.
D. The legs of 45 ° −45 °−90 ° triangle are congruent.
For items 27 – 30, refer to the given ∆ SHR ∆ WIN .
27. Which of the following is NOT a pair of corresponding vertices?
A. S ↔W B. R↔ N C. H↔ N D. H ↔ I
28. Which of the following pair of angles are congruent?
A. LS≅ LN B. LH≅ LW C. LR≅ LI D. LS≅ LW
29. Which of the following proportions is correct?
SH HR SR HR HR SH SN WN
A. = B. = C. = D. =
WI ¿ WI RN WN ¿ RW HI
30. If SH = 3, HR = 5, and WI =6, what is the measure of IN?
A. 8 B. 9 C. 10 D. 11
31. In a 30°−60 °−90 °, if the shorter leg is equal to 5, what is the length of the longer leg?
A. 5√ 2 B. 5√ 3 C. 10 D. 5

32. What is the ratio of the 30°−60 °−90 °triangle in increasing order?
A. 1:√ 3 :2 B. 1:2 : √ 3 C. 1:2 : √ 2 D. 1:√ 2: 2
60°
x
33. Refer to the figure at the right, how long is the measure of x?
A. 3√ 3 m B. 6 m. C. 3m. D. 3√ 2m.
3m.
34. Given ∆ YOU , find the value of x. O
A. 5√ 3 B. 3√ 5 C. 9√ 5 D. 15
x
Y
35. It is the longest side of a right triangle. 6 3 U
A. leg B. altitude C. base D. hypotenuse 9 5

36. If a man walks 7km east and then 6 km south, how far is he from the point where he started? n
A. √ 42 km B. √ 37 km C. √ 85 km D. √ 51 km
37. Which of the following is NOT a proportion?
5 50 2 10 7 14 1 5
A. = B. = C. = D. =
6 60 10 50 14 28 10 25

38. What do we call to the uniform ratio k of the corresponding proportional sides of polygons?
A. Ratio B. Scale Factor C. Dilation D. Geometric mean
N
M
 A
39. Given ∆ MEL ∆ BEN , what is the mL1 if measure of L2 is 65°?
A. 25° B. 45° C. 65° D. 90° 2 1
E B
L
40. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. What theorem is
stated?
A. SAS Similarity Theorem B. TABT c. TPT D. Pythagorean Theorem