DEPARTMENT OF EDUCATION
Division of Quezon
QUEZON NATIONAL HIGH SCHOOL
Lucena City
MATHEMATICS 9
Summative Test 1
Fourth QUARTER
NAME:
GRADE & SECTION:
I.
DATE:
TEACHER:
SCORE:
Read each item carefully. Write the letter of the correct answer on the space provided before each number.
1. Which of the following mathematical statement states that two ratios are equal: 𝑎 ∶ 𝑏 = 𝑐 ∶ 𝑑, where b ≠ 0 and
d ≠ 0?
a. Ratio
b. Extremes
c. Proportion
d. Term
2. What is the ratio of similarity if 𝜟𝑴𝑨𝑵 ~ 𝜟𝑩𝑶𝒀?
2
3
a.
c.
3
3
5
b.
d.
2
2
5
3. Two triangles are similar if two angles of one triangle are
angles of another triangle.
a. Supplementary
b. Complementary
c. Not congruent
to two
d. Congruent
4. In the figure, there are three similar right triangles by Right Triangle
Proportionality Theorem. Name the triangle that is missing in this statement:
𝜟𝑯𝑶𝑷 ~ _______ ~𝜟𝑶𝑬𝑷.
a. ΔOEH
c. ΔHOP
b. ΔHOE
d. ΔHEO
5. What do you call the longest side of a right triangle?
a. Leg
b. corresponding side c. hypotenuse
d. altitude
6. In the figure at the right, which relationship is true?
a. 𝑐 2 + 𝑎2 = 𝑏 2
c. 𝑐 = √𝑎2 + 𝑏 2
b. 𝑎2 = 𝑐 2 − 𝑏 2
d. 𝑏 = √𝑎2 − 𝑐 2
7. Which of the following is NOT length of sides of a right triangle?
a. 6, 8, 9
b. 5, 5, 5√2
c. 3, 4, 5
d. 30, 40, 50
8. If ∆𝑨𝑶𝑩~∆𝑫𝑶𝑪 are similar, which similarity theorem or postulate proves it?
a. AA Similarity Theorem
c. SSS Similarity Theorem
b. SAS Similarity Theorem
d. AAA Similarity Theorem
9. Which of the following is NOT a Pythagorean Triple?
a. 5, 12, 13
b. 7, 8, 10
c. 26√2, 13√2, 13√6
d. 10√2, 10√2, 20
10. Using the figure, which proportions are TRUE?
𝑎
𝑏
𝑏
𝑒
I.
=𝑐
III.
=𝑓
𝑑
𝑎+𝑏
𝑐
𝑑
𝑓
=𝑒
a. I and II only
b. b. I and IV only
II.
IV.
𝑏
𝑎+𝑏
𝑐
= 𝑐+𝑑
c. II and III only
d. III and IV only
11. The lengths of the sides of a triangle are 6 cm, 10 cm, and 13 cm. What kind of a triangle is it?
a. Regular Triangle
b. Obtuse Triangle
c. Right Triangle
d. Acute Triangle
12. What theorem will you use to find the diagonal of a 10 cm by 8 cm rectangle?
a. Triangle Angle Bisector Theorem
c. Triangle Proportional Theorem
b. Triangle Similarity Theorem
d. Right Triangle Proportionality Theorem
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13. Given: ∆𝑷𝑸𝑹~∆𝑿𝒀𝒁 𝑎𝑛𝑑
triangles?
a. AA Similarity Theorem
b. SSS Similarity Theorem
𝑷𝑸
𝑿𝒀
=
𝑸𝑹
𝒀𝒁
=
𝑷𝑹
,
𝑿𝒁
which of the following justifies the similarity between the two
c. AAA Similarity Theorem
d. SAS Similarity Theorem
14. In a 𝟒𝟓° − 𝟒𝟓° − 𝟗𝟎° triangle, the side opposite the 45° is
a. Equal to
b. Half
c.
√2
2
the hypotenuse.
𝑡𝑖𝑚𝑒𝑠
.
√3
2
𝑡𝑖𝑚𝑒𝑠
15. The lengths of the sides of one triangle are x, 10, and 8. The corresponding lengths of sides of a similar
triangle are 18, 15, and y. What is the value of y?
a. 15
b. 12
c. 10
d. 8
16. What is the perimeter of a 𝟑𝟎° − 𝟔𝟎° − 𝟗𝟎° triangle whose shorter leg is 5 inches long?
a. 5√3 𝑐𝑚
b. 5 + 5 √3 𝑐𝑚
c. 10 + 5 √3 𝑐𝑚
d. 15 + √3 𝑐𝑚
17. ∆BRY ~ ∆ ANT .Which ratio of sides gives the scale factor?
a.
b.
𝑁𝑇
𝐴𝑁
𝑁𝑇
𝐴𝑇
c.
d.
𝐴𝑇
𝐵𝑌
𝑁𝑇
𝑅𝑌
18. What is the value of x?
a. 3
c. 6
b. 3 √2
d. 6 √2
19. If ∆𝐴𝐵𝐶 is a right triangle, what is the length of the side opposite ∠𝐵 if 𝑚∠𝐵 = 90° and the lengths of the
other sides are 12 cm and 16 cm?
a. 26 cm
b. 24cm
c. 22 cm
d. 20 cm
20. In the figure, if AE = 8, AB = 4, BC = 10, ED = 3. What is the length
of BD and DC?
a. BD = 3, DC = 3
c. BD = 1.5, DC = 2
b. BD = 6, DC = 4
d. BD = 5.7, DC = 7.5
21. The segment 15 cm long is divided into two parts in the ratio 2:3. What is the length of each part?
a. 3 and 6
b. 1 and 36
c. and 9
d. 3 and 9
22. A rectangular field is 50 m wide by 100 m long. How long is the diagonal path connecting the two opposite
corners of the field?
a. 111.80 m
b. 12 500 m
c. 86.60 m
d. 7 500 m.
23. Given the diagram on the right, calculate the distance AB across the lake.
a. 15.66 m
c. 61.38 m
b. 159.68 m
d. 27.28 m
24. If the bottom of a 5-meter ladder is 2 meters from a wall, how high on
the wall does it reach?
a. √29 m
c. √25 m
b. b. √23 m
d. √21 𝑚
25. Two trees cast shadows on the ground as shown. The smaller
tree is 17m high. What is the height of the taller tree?
a. 7.06 m
c. 35.68 m
b. 9.07 m
d. 31. 88 m
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