ALGEBRA PRACTICE TEST
GRADE 8
Geometry & Probability
Name: Score:
Multiple Choice: Choose the letter of the correct answer. Write your answer in the space provided for.
1. What theorem that defines the sum of the lengths of any two sides is greater than the length of the third
side?
a. Exterior Angle Inequality Theorem c. Triangle Inequality Theorem 1. ____
b. Hinge Theorem d. Converse of the Hinge Theorem
2. What theorem that supports the illustration and statement below?
“If 𝑚∠1 > 𝑚∠3 then 𝑚∠1 > 𝑚∠4.”
a. Triangle Inequality Theorem 2. ____
b. Hinge Theorem
c. Exterior Angle Inequality Theorem
d. Converse of the Hinge Theorem
3. What theorem that best describes the illustration at the right?
a. Hinge Theorem c. Exterior Angle Inequality Theorem 3. ____
b. Converse of the Hinge Theorem d. Triangle Inequality Theorem
4. What theorem best describes the statement below?
“If ̅̅̅̅ 𝑋𝑌, ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅̅ 𝑌𝑍 > ̅̅̅̅
𝑋𝑍, 𝑎𝑛𝑑 ̅̅̅̅ 𝐵𝐶 , then 𝑚∠𝑋 > 𝑚∠𝐴”
a. Hinge Theorem c. Converse of the Hinge Theorem 4. ____
b. Exterior Angle Inequality Theorem d. Triangle Inequality Theorem
5. Which of the following lengths can form a triangle? 5. ____
a. 6cm, 7cm, 14 cm c. 5cm, 5cm, 10cm
b. 3cm, 7cm, 8cm d. 5cm, 6cm, 10cm
̅̅̅̅ > 𝐷𝑁
6. Will you able to conclude that 𝐷𝑌 ̅̅̅̅ based on the illustration in at the right? 6. ____
a. Yes, I will
b. No, I won’t.
c. It is impossible to decide.
d. It depends on which statement is left out.
7. From the inequalities in the triangles shown, a conclusion can be reached using the converse of hinge
theorem. Which of the following is the last statement? 7. ____
̅̅̅̅ ≅ 𝐺𝐾
a. 𝐺𝐾 ̅̅̅̅
b. 𝐺𝐻 ≅ ̅̅̅
̅̅̅̅ 𝐺𝐽
c. 𝑚∠1 > 𝑚∠2
d. 𝑚∠2 > 𝑚∠1
8. Bikers Justin and Carl with a uniform speed in opposite directions- Justin, eastward whereas Carl,
westward. After walking three kilometers each, both of them take left turns at different angles. Justin at an
angle of 30° and Carl at 40° covers four kilometers. Both continue hiking before taking a rest. Which hiker is
farther from their point of origin?
a. Justin c. It cannot be determined. 8. ____
b. Carl d. Justin is as far as Carl from the rendezvous.
For numbers 9 to 12, refer to the illustration at the right.
Given: ∆𝐴𝑅𝑇 with I as the midpoint of 𝑇𝑅 𝑅𝑁 ≅ ̅𝑇𝑆
̅̅̅̅ , ̅̅̅̅ ̅̅̅, and IN> IS.
Prove: AT>AR
GRADE 8
Geometry & Probability
Name: Score:
Multiple Choice: Choose the letter of the correct answer. Write your answer in the space provided for.
1. What theorem that defines the sum of the lengths of any two sides is greater than the length of the third
side?
a. Exterior Angle Inequality Theorem c. Triangle Inequality Theorem 1. ____
b. Hinge Theorem d. Converse of the Hinge Theorem
2. What theorem that supports the illustration and statement below?
“If 𝑚∠1 > 𝑚∠3 then 𝑚∠1 > 𝑚∠4.”
a. Triangle Inequality Theorem 2. ____
b. Hinge Theorem
c. Exterior Angle Inequality Theorem
d. Converse of the Hinge Theorem
3. What theorem that best describes the illustration at the right?
a. Hinge Theorem c. Exterior Angle Inequality Theorem 3. ____
b. Converse of the Hinge Theorem d. Triangle Inequality Theorem
4. What theorem best describes the statement below?
“If ̅̅̅̅ 𝑋𝑌, ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅ 𝐴𝐶 ≅ ̅̅̅̅ 𝑌𝑍 > ̅̅̅̅
𝑋𝑍, 𝑎𝑛𝑑 ̅̅̅̅ 𝐵𝐶 , then 𝑚∠𝑋 > 𝑚∠𝐴”
a. Hinge Theorem c. Converse of the Hinge Theorem 4. ____
b. Exterior Angle Inequality Theorem d. Triangle Inequality Theorem
5. Which of the following lengths can form a triangle? 5. ____
a. 6cm, 7cm, 14 cm c. 5cm, 5cm, 10cm
b. 3cm, 7cm, 8cm d. 5cm, 6cm, 10cm
̅̅̅̅ > 𝐷𝑁
6. Will you able to conclude that 𝐷𝑌 ̅̅̅̅ based on the illustration in at the right? 6. ____
a. Yes, I will
b. No, I won’t.
c. It is impossible to decide.
d. It depends on which statement is left out.
7. From the inequalities in the triangles shown, a conclusion can be reached using the converse of hinge
theorem. Which of the following is the last statement? 7. ____
̅̅̅̅ ≅ 𝐺𝐾
a. 𝐺𝐾 ̅̅̅̅
b. 𝐺𝐻 ≅ ̅̅̅
̅̅̅̅ 𝐺𝐽
c. 𝑚∠1 > 𝑚∠2
d. 𝑚∠2 > 𝑚∠1
8. Bikers Justin and Carl with a uniform speed in opposite directions- Justin, eastward whereas Carl,
westward. After walking three kilometers each, both of them take left turns at different angles. Justin at an
angle of 30° and Carl at 40° covers four kilometers. Both continue hiking before taking a rest. Which hiker is
farther from their point of origin?
a. Justin c. It cannot be determined. 8. ____
b. Carl d. Justin is as far as Carl from the rendezvous.
For numbers 9 to 12, refer to the illustration at the right.
Given: ∆𝐴𝑅𝑇 with I as the midpoint of 𝑇𝑅 𝑅𝑁 ≅ ̅𝑇𝑆
̅̅̅̅ , ̅̅̅̅ ̅̅̅, and IN> IS.
Prove: AT>AR
