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WorksheetsPeriodic Test in Mathematics 8
Total questions: 50
Worksheet time: 48mins
What do you call the statements that can only be described and not defined?
axioms
defined terms
theorems
undefined terms
Which of the following is a commutative axiom?
2 + 3 = 2 + 3
2 + 3 = 3 + 2
2 ∙ 3 = 2 ∙ 3
(2 + 3) = 2(3) + 3(2)
Which of the following illustrates Multiplicative axiom?
if 𝑎 = 𝑏, then 𝑏 = 𝑎
if 𝑎 = 𝑏 and 𝑏 = 𝑐, then 𝑎 = 𝑐
if 𝑎 = 𝑏, then 𝑎 + 𝑐 = 𝑏 + 𝑐
if 𝑎 = 𝑏, then, 𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐
Name the property which justifies the following conclusion. Given: If 5𝑥 - 5 = 10 Conclusion: then 5𝑥 = 15
Existence of Additive Inverse.
Existence of Multiplicative Identity.
Existence of Multiplicative Inverse.
Existence of Additive Inverse and Additive Identity.
Which of the following illustrates reflexive property?
(𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷
(𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = 𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷
(𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = (𝐵𝐶 + 𝐴𝐵) + 𝐶𝐷
(𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = 𝐶𝐷 + (𝐴𝐵 + 𝐵𝐶)
Baguio City is the summer capital of the Philippines. Which of the following best describes the statement?
The statement is obviously false.
The statement cannot be proven to be true or false.
The statement needs to be formally proven to be accepted as true.
The statement does not need to be formally proven and is accepted as true.
What undefined term is represented by a dot?
point
line
plane
angle
Which of the following does not represent a plane?
tip of a pen
top of the table
cover page of a book
faces of a rectangular box
How do you call a line perpendicular to a given segment which divides it into two equal line segments?
diagonals
line segment
congruent segments
perpendicular bisector
What axioms of equality do the illustration below represent?
reflexive property
substitution property
symmetric property
transitive property
The angles inside the triangular garden ABC are all 60°. To be able to find the length of the sides of the garden, Mary measured the sides as follows; 2.5 𝑚, 3 𝑚 and 5 𝑚. Did Mary measure it correctly?
No, because an equiangular triangle is also equilateral.
No, because two sides of an equiangular triangle must be equal.
Yes, because a triangle is not equilateral if it is equiangular.
Yes, because not all equiangular triangles are equilateral.
You are tasked to make a triangular picture frame and your teacher gives you five sticks of the same length and one shorter length. What triangle can you make out of the materials given if you are not allowed to cut the stick?
equilateral triangles
isosceles and equilateral triangles
scalene and isosceles triangles
The materials cannot form a triangle
Which of the following statements is not true about congruent triangles?
They are dissimilar.
They are coinciding.
They have the same size and shape.
They have corresponding congruent parts.
If 𝛥𝐹𝑅𝑌 ≅ 𝛥𝐻𝑂𝑇, which segment is congruent to 𝑅𝑌̅̅̅̅?
𝐻𝑇̅̅̅̅
𝐹𝑌̅̅̅̅
𝑂𝑇̅̅̅̅
𝑅𝐹̅̅̅̅
If 𝛥𝑆𝐼𝑇 ≅ 𝛥𝐻𝑂𝑃, then what angle corresponds to ∠𝑇?
∠𝐻
∠𝐼
∠𝑃
∠𝑆
Which of the following shows a pair of congruent triangles?
𝛥𝐹𝐼𝑉 ≅ 𝛥𝐼𝑉𝐸
𝛥𝐼𝐹𝑉 ≅ 𝛥𝐼𝑉𝐸
𝛥𝐹𝐼𝑉 ≅ 𝛥𝐸𝐼𝑉
𝛥𝐼𝐹𝑉 ≅ 𝛥𝑉𝐼𝐸
What would be the name of the congruent triangles given their corresponding sides: 𝐿𝑂̅̅̅ ≅ 𝑅𝑃̅̅̅̅, 𝑀𝑂 ̅̅̅̅̅ ≅ 𝑄𝑃̅̅̅̅, ̅𝐿𝑀̅̅̅ ≅ 𝑅𝑄̅̅̅̅?
𝛥𝐿𝑂𝑀 ≅ 𝛥𝑄𝑃𝑅
𝛥𝑂𝑀𝐿 ≅ 𝛥𝑃𝑄𝑅
𝛥𝑀𝑂𝐿 ≅ 𝛥𝑅𝑄𝑃
𝛥𝐿𝑀𝑂 ≅ 𝛥𝑃𝑄𝑅
Which of the following illustrations below best describe the congruent triangle in item 17?
Which of the illustrations below represents the ASA Congruence Postulate?
Given ∆LOT, what is the included angle between ̅𝐿𝑂̅̅̅ and 𝑂𝑇̅̅̅̅?
∠L
∠O
∠T
∠ TLO
What other pair of corresponding congruent part is needed to make the two triangles congruent by ASA Congruence Postulate?
∠G and ∠T
∠I and ∠A
∠B and ∠F
∠B and ∠A
What other pair of corresponding congruent part is needed to make the two triangles congruent by SAS Congruence Postulate?
𝐼𝐺̅̅̅ and 𝐴𝑇̅̅̅̅
̅𝑇𝐹̅̅̅ and 𝑇𝐴̅̅̅̅
̅𝐵𝐼̅̅ and 𝐹𝐴̅̅̅̅
𝐺𝐵̅̅̅̅ and ̅𝑇F
What other pair of corresponding congruent sides is needed using SSS congruence postulate if ∆PUB≅ ∆NET?
A. BP ≅ NE B. BP ≅ TN C. NT ≅ PU D. NT ≅ UB
Which pair of corresponding congruent angles is needed using SAS congruence postulate if ∆PUB≅ ∆NET?
∠U ≅ ∠ N
∠B ≅ ∠ T
∠P ≅ ∠E
∠E ≅ ∠U
Given that ∆HIJ ≅ ∆LMN, what angle corresponds to ∠J?
∠H
∠I
∠M
∠N
If ∆LUV ≅ ∆YAH, then ∆HAY is congruent to ____.
∆AYH
∆LVU
∆UVL
∆VUL
Which of the following is a congruence statement in Figure 1?
∆BVS ≅ ∆VLB
∆ISV ≅ ∆BNL
∆SVI ≅ ∆LBN
∆VSI ≅ ∆NBL
Live has two triangular vegetable gardens shown in Figure 2. He wants to fence them to protect his crops. It takes 7 m of fencing material for one garden. What is the total length of fencing material needed if the two gardens are of the same size and shape?
7 m
14 m
21m
28 m
Figure 3 shows that ∆BEN is congruent to ∆IVR. Find the value of x.
5
6
13
30
You are making party hats for your bestfriend's birthday. The measurements are shown in Figure 4. Find the value of x.
3
5
7
9
Which of the theorems below states that: "If two angles and a non-included side of one triangle are congruent to the corresponding two angles and a non-included side of another triangle, then the triangles are congruent."?
HyA Congruence Theorem
HyL Congruence Theorem
LL Congruence Theorem
AAS Congruence Theorem
Which of the following pairs of triangles below are congruent and can be proved by SAS Congruence?
i and ii
ii and iii
iii
i, ii, and iii
In the figure at the right, 𝑶𝑻̅̅̅̅ is a perpendicular bisector of 𝑯𝑺 ̅̅̅̅ at T. What triangle congruence theorem can be used to prove that ∆𝐻𝑂𝑇 ≅ ∆𝑆𝑂𝑇?
LL Congruence Theorem
HyL Congruence Theorem
HyA Congruence Theorem
AAS Congruence Theorem
Which statement is NOT sufficient to prove the congruence of two triangles?
Two angles and the included side of one triangle are congruent respectively to the two angles and the included side of another triangle.
Two sides of one triangle are congruent respectively to the two sides of another triangle
Two angles and the non-included side of one triangle are congruent respectively to the two angles and the non-included side of another triangle.
Three sides of one triangle are congruent respectively to the three sides of another triangle.
You are tasked to make a design of the flooring of your barangay hall using triangles. The available materials are square tiles. How are you going to make the design?
Apply triangle congruence by SSS
Apply triangle congruence by ASA.
Apply triangle congruence by SAS.
Apply triangle congruence by AAS.
The figure at the right shows a ring with a rhombus-shaped diamond. 𝐼𝐺 divides the diamond into two congruent triangles. What reason will justify that IRG ≅ 𝐼𝑁𝐺?
Adjacent angles congruent
Vertical angles are congruent
Alternate interior angle congruent
Opposite angles of a rhombus are congruent
∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 are isosceles right triangles. 𝐴𝐵̅̅̅̅ ≅ 𝐷𝐸̅̅̅̅ and 𝐴𝐶̅̅̅̅ ≅ 𝐷𝐹̅̅̅̅, which of the following statements is true by CPCTC?
A. AC ≅ EF B. BC ≅ EF C. CA ≅ EF D. CB ≅ FD
In ∆𝐽𝑂𝑌, let S be a midpoint of 𝐽𝑌̅̅̅ and 𝑂𝑆 ̅̅̅̅ ⊥ 𝐽𝑌̅̅̅. What theorem or postulate can justify that ∆𝐽𝑂𝑆 ≅ ∆𝑌𝑂𝑆?
AAS
ASA
LL
HyL
Refer to item number 38, what are the other corresponding angles that are congruent by CPCTC?
I only
II only
I and II only
II and III only
In ∆𝑊𝐸𝑇 and ∆𝐷𝑅𝑌, 𝑊𝐸 ̅̅̅̅̅ ≅ 𝐷𝑅̅̅̅̅, 𝐸𝑇̅̅̅̅ ≅ 𝑅𝑌̅̅̅̅ and 𝑊𝑇 ̅̅̅̅̅ ≅ 𝐷𝑌̅̅̅̅. By SSS Congruence Postulate, we can say that ∆𝑊𝐸𝑇 ≅ ∆𝐷𝑅𝑌. Which congruence statement/s of the other corresponding parts of the two triangles is/are true?
I angle W = angle D II angle E = angle R III angle T = angle Y
I only
II only
II and III only
I, II and III
The figure at the right is formed by overlapping triangles. Which of the following congruence statements is true?
∆𝐶𝐺𝑆 ≅ ∆𝐴𝐸𝑁
∆𝐶𝐺𝑆 ≅ ∆𝐻𝐸𝑁
∆𝑆𝐶𝐺 ≅ ∆𝐴𝐸𝑁
∆𝑆𝐶𝐺 ≅ ∆𝑁𝐸𝐻
Which theorem or postulate can be used to show that ∆𝐺𝐸𝐷 ≅ ∆𝐼𝐷𝐸?
AAS Congruence Theorem
ASA Congruence Postulate
HL Congruence Theorem
SAS Congruence Postulate
If ∆𝐸𝐻𝑇 ≅ ∆𝐴𝑇𝐻, which congruence statement of the corresponding parts of the two triangles is true?
∠𝐻𝐸𝑇 ≅ ∠𝐴𝐻𝑇
∠𝑇𝐸𝐻 ≅ ∠𝐸𝑇𝐴
∠𝐻𝐸𝑇 ≅ ∠𝑇𝐴𝐻
∠𝑇𝐻𝐸 ≅ ∠𝑇𝐻 𝐴
Which of the following is true about an angle bisector?
It divides an angle into halves.
It divides an angle at 90⁰.
It divides an angle at 45⁰.
It divides an angle into three parts.
What do you call the segments or lines that intersect forming a 90-degree angle?
angle bisector
auxiliary lines
skew segments/lines
perpendicular segments/lines
Which among the following theorems of triangle congruence can be used to prove that ∆𝐻𝐸𝑃 ≅ ∆𝐻𝑂𝑃?
AAS
HyA
LA
LL
Which of the following is true about 𝑃𝐻̅̅̅̅?
𝑃𝐻̅̅̅̅ bisects ∠𝐸𝑂𝑃
𝑃𝐻̅̅̅̅ bisects ∠𝑃𝐸𝑂
𝑃𝐻̅̅̅̅ bisects ∠𝐸𝑃𝑂
𝑃𝐻̅̅̅̅ bisects ∠𝑃𝑂E
Which of the following reasons justifies 𝑃𝐻̅̅̅̅ ≅ 𝑃𝐻̅̅̅̅?
Definition of congruent segments
Definition of Perpendicular
Reflexive Property
Congruent Parts of Congruent Triangles are Congruent
If you put together the two triangles in such a way that 𝐺𝐸̅̅̅̅ of ⊿𝐺𝐸𝐷 coincides with the 𝐺𝐸̅̅̅̅ of ⊿ 𝐺𝐸𝐹, which of the following is NOT TRUE about 𝐺𝐸̅̅̅̅ to ∠𝐷𝐺𝐹?
𝐺𝐸̅̅̅̅ bisects ∠𝐷𝐺𝐹
𝐺𝐸̅̅̅̅ is in the interior of ∠𝐷𝐺𝐹
𝐺𝐸̅̅̅̅ is in the exterior of ∠𝐷𝐺𝐹
𝐺𝐸̅̅̅̅ is the angle bisector of ∠𝐷𝐺𝐹
If you put together the two triangles in such a way that 𝐺𝐸̅̅̅̅ of ⊿𝐺𝐸𝐷 coincides with the 𝐺𝐸̅̅̅̅ of ⊿ 𝐺𝐸𝐹, what is the relationship of 𝐺𝐸̅̅̅̅ and 𝐷𝐹̅̅̅̅?
𝐺𝐸̅̅̅̅ bisects 𝐷𝐹̅̅̅̅
𝐺𝐸̅̅̅̅ is congruent to 𝐷𝐹̅̅̅̅
𝐺𝐸̅̅̅̅ do not lie in side 𝐷𝐹̅̅̅̅
𝐺𝐸̅̅̅̅ is parallel to 𝐷𝐹̅̅̅̅
