Learning Activity Sheets (LAS) Grade 8 -Mathematics

Name:_______________________________ Date:______________________ Score:__________

Describing a Mathematical System

A. DIRECTIONS: Fill in the blanks with the correct words, or phrases to make the statements meaningfully
correct. You may choose from the box below.
angle parallel lines point right angle
line perpendicular lines postulates theorems
line segment plane ray undefined terms

1. A ____________ has no dimension. It has an exact location in space.

2. An ___________ is a figure formed by two noncollinear rays with a common endpoint called the
vertex.
3. Two lines that intersect which form right angles are called __________________.
4. Statements proven from definitions, postulates, or using operations from facts that were already known
are called _______________.
5. A ____________ is a collection of points along a straight path that extends endlessly in both
directions.
6. An angle whose measure is exactly 90° is called a ____________.
7. Statements that are assumed to be true without proof are called __________.
8. A ___________ extends infinitely in two dimensions. It has no thickness and is named by three points
that do not lie on the same line.
9. A _______________ is a part of a line having two endpoints.
10. Two lines that lie in the same plane and do not intersect are called ______________.

B. DIRECTIONS: Underline the statement, group of words, or phrases that describe a component of a
mathematical system. Identify the component you underlined and write your answer on the space
provided before each number.
____________1. Marikina City is known as the Shoe Capital of the Philippines.
____________2. Some people believe that COVID-19 is not a deadly virus.
____________3. If you shoot a laser towards the sky you can see a line that extends infinitely more than
what your naked eye can see.
____________4. The hinge of the door when being opened shows different measurements of angles.
____________5. According to studies, staying indoors and frequently washing of hands can help prevent the
spread of virus.

Specific Week: Week 1

Target Competency: Describes a mathematical system.
Note to the Teacher: This is for summative assessment.
(This is a Government Property. Not For Sale.)
Learning Activity Sheets (LAS) Grade 8 -Mathematics
Mathematical System: Postulates and Proof
C. DIRECTION: Identify the properties exhibited in each item.

1. If x + y = 3, then x + y – 3 = 0 __________________________________________________
2. If a + b = c and c – 7 = d, then (a + b) – 7 = d ______________________________________
𝑚
3. If = 5, then m = 20 _______________________________________________________
4
4. If k + 9 = 9, then 9 = k + 9. _________________________________________________
5. If 12xy = x – y + 5, then x – y + 5 = 12xy __________________________________________
6. If x – 100 = y + 10, then x = y + 110 _____________________________________________
7. If 7xy = 49x2 and x ≠ 0, then y = 7x ______________________________________________
8. If 2xy(x + 3y - 1), then 2x2y + 6xy2 – 2xy __________________________________________
9. ∠x = ∠x __________________________________________________________________
10. If 2x + 7y = 3z and 3z = 2y + 5, then 2x + 7y = 2y + 5 __________________________________

D. DIRECTION: Complete the given two-column proof with the correct property.
Given: 4 (2x + y – 3) = 10x + 2y
Prove: y = x + 6
Statement Reason
1. 4 (2x + y – 3) = 10x + 2y GIVEN
2. 8x + 4y – 12 = 10x + 2y

3. 8x + 4y = 10x + 2y + 12

4. 4y = 2x + 2y +12

5. 2y = 2x + 12

6. y = x + 6

Specific Week: Week 2

Target Competency: illustrates the need for an axiomatic structure of a mathematical system in general, and in
Geometry in particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems.
Note to the Teacher: This is a summative assessment.
(This is a Government Property. Not For Sale.)
Learning Activity Sheets (LAS) Grade 8 -Mathematics
Given: ∠a and ∠b are vertical angles. a
Prove: ∠a ≅ ∠b
b

Statement Reason
1. ∠a and ∠b are vertical angles GIVEN
2.

3.

4.

5.

6.

E. Analyze the way of transformation in each figure to show congruency. Distinguish if it is ROTATION,
TRANSLATION or REFLECTION.

_____________________ _____________________ ____________________

F. Tell which postulate will conclude that the following pairs of triangles are congruent.

1. 2. 3. 4.
____________ ____________ ____________ ___________

G. Determine the additional corresponding parts needed to make the triangles congruent by using the
specified congruence postulates.

1. 2. 3.
a. ASA _______ a. SAS _______ a. SSS _______
b. SAA _______ b. SSS _______ b. SAS _______
Specific Week: Week 2
Target Competency: illustrates the need for an axiomatic structure of a mathematical system in general, and in
Geometry in particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems; illustrate triangle
congruence; and illustrate the SAS, ASA and SSS congruence postulates.
Note to the Teacher: This is a summative assessment.
(This is a Government Property. Not For Sale.)
Learning Activity Sheets (LAS) Grade 8 -Mathematics
H. Encircle the letter of your answer.

̅̅̅̅?
1. If ∆PGO ≅ ∆SRO, what is the side corresponding to GO
̅̅̅̅
a. PG ̅̅̅̅
b. RO ̅̅̅̅
c. SO d. ̅̅
SR̅̅

2. In ∆CAR, which angle is between ⃗⃗⃗⃗⃗

𝑅𝐶 and ⃗⃗⃗⃗⃗
𝑅𝐴?
a. ∠A b. ∠C c. ∠R d. none

̅̅̅̅ = 𝑅𝑂
3. Given in ∆RPO, 𝑅𝑃 ̅̅̅̅. If m∠P = 80, find the measure of ∠R.
a. 20 b. 80 c. 100 d. 180

4. If ∆FRY ≅ ∆DRY, what congruent part shows reflexive property?

̅̅̅̅ ≅ ̅̅̅̅
a. FY RY b. ̅̅̅̅
RY ≅ ̅̅̅̅
RY c. ̅̅̅̅
YR ≅ ̅̅̅̅
YD ̅̅̅̅ ≅ RD
d. RF ̅̅̅̅

̅̅̅̅ ≅ PO
5. Complete the statement by symmetric property: If RE ̅̅̅̅, then ______.
̅̅̅̅ ̅̅̅̅
a. RE ≅ OP ̅̅̅̅ ̅̅̅̅
b. ER ≅ PO c. PO ≅ ̅̅̅̅
̅̅̅̅ RE d. ̅̅̅̅
RE ≅ ̅̅̅̅
PO

6. What angle in ∆TAR is congruent to ∠JYA if ∆JAY ≅ ∆ANE and ∆ANE ≅ ∆TAR?
a. ∠TAR b. ∠RAT c. ∠TRA d. ∠ATR

̅̅̅̅ if ∆FAY ≅ ∆BOL and ∆BOL ≅ ∆QUE?

7. What side in ∆QUE is congruent to FA
̅̅̅̅
a. UE ̅̅̅̅
b. EU c. ̅̅̅̅
QE d. ̅̅̅̅
QU

8. If ∆ZAP ≅ ∆BOR, which congruency statement is true?

a. ̅ZP
̅̅̅ ≅ ̅̅̅̅
OR b. ∠APZ ≅ ∠ROB c. ∠PAZ ≅ ∠ROB d. ̅̅̅̅
ZA ≅ ̅̅̅̅
OR

9. If ∆ABC and ∆ZTE are congruent by SAS Postulate, what congruency statement is needed if ̅̅̅̅
AB ≅ ̅̅̅
ZT̅ and
̅̅̅̅ ≅ TE
BC ̅̅̅̅?
a. ∠B ≅ ∠T b. ∠A ≅ ∠Z c. ∠C ≅ ∠E d. ∠A ≅ ∠T

10. ∆ABC and ∆CDA are congruent by what postulate or theorem?

a. SAS b. ASA c. AAS d. SSS

Specific Week: Week 2

Target Competency: illustrate triangle congruence; and illustrate the SAS, ASA and SSS congruence postulates.
Note to the Teacher: This is a summative assessment.
(This is a Government Property. Not For Sale.)