REVIEWER in PREFINALS in MATHEMATICS 8

Liam is building a triangular tent with sides measuring 6 cm, 8 cm, and 10 cm. Which inequality theorem will he apply to determine the largest angle in the triangle?

• Angle-side 

• Exterior angle

• Hinge theorem

• Side-angle

Sofia is creating a triangular garden with angles measuring 40°, 60°, and 80°. Which side of the triangle is the longest based on the Angle-Side Inequality Theorem?

• The side opposite the 40° angle

• The side opposite the 60° angle

• The side opposite the 80° angle

• All sides are equal in length

Mia, an aspiring architect, is designing a triangular window for a new house. She has wooden beams of different lengths and wants to ensure that they form a valid triangle before assembling them. She recalls the Triangle Inequality Theorem 3 (S₁ + S₂ > S₂), which states that the sum of any two sides of a triangle must be greater than the third side.

Mia has three beams measuring 5 cm, 8 cm, and 12 cm. Can she form a triangular window with these lengths?

• Yes, because the sum of any two sides is greater than the third.

• No, because 5 + 8 is not greater than 12.

• Yes, because all three sides are different.

• No, because all three sides must be equal.

Mia, an aspiring architect, is designing a triangular window for a new house. She has wooden beams of different lengths and wants to ensure that they form a valid triangle before assembling them. She recalls the Triangle Inequality Theorem 3 (S₁ + S₂ > S₂), which states that the sum of any two sides of a triangle must be greater than the third side.

What calculation should she do?

• 6 + 9 > 14, 6 + 14 > 9, and 9 + 14 > 6

• 9 - 6 > 14, 14 - 6 > 9, and 14 - 9 > 6

• 6 x 9 > 14, 6 x 14 > 9, and 9 x 14 > 6

• 9 ÷ 6 > 14, 14 ÷ 6 > 9, and 14 ÷ 9 > 6

A traffic engineer is designing a triangular road intersection. At one of the turns, the two interior angles are 45° and 55°. The engineer needs to determine whether the turn is sharp or wide.

According to the Exterior Angle Inequality Theorem, how does the exterior angle at this turn compare to the other two interior angles?

• It is smaller than both interior angles.

• It is equal to the larger interior angle

• it is greater than each interior angle

• It is the sum of the two interior angles

The two classrooms have the same type of doors that open outward. In the morning:

Classroom A’s door is opened at a 75° angle

Classroom B’s door is opened at a 45° angle

Assuming both doors are of equal width, which of the following is true?

• Classroom A’s door extends farther into the hallway than Classroom B’s door.

• Classroom B’s door extends farther into the hallway than Classroom A’s door.

• Both doors extend equally into the hallway.

• The door frame determines how far the door extends, not the angle.

Marie and Jake are both cutting paper using identical scissors. Sophia opens her scissors wider, while Jake keeps his scissors nearly closed.

Based on the Converse of the Hinge Theorem, which statement is true?

• Marie’s scissor blades create a longer cut than Jake’s.

• Jake’s scissor blades create a longer cut than Marie’s.

• Both scissor blades create cuts of the same length.

• The cut length depends only on the sharpness of the blades.

Richard is a landscaper who designs and creates outdoor spaces, such as gardens, paths, and water features. He is tasked to design a triangular flower garden with sides measuring 5 m, 9 m, and 12 m (see Figure 1). He needs to arrange the angles from largest to smallest to determine where to place decor Which order correctly arranges the angles from largest to smallest?

• ∠A, ∠B, ∠C

• ∠B ∠C, ∠A

• ∠C, ∠B, ∠A

• ∠A, ∠C, ∠B

Billboards are large outdoor advertisements that are used to promote a brand, product, or service. A company is installing a triangular billboard for better visibility. The angles of the triangle measure 35°, 90°, and 55° (see figure 2). To understand the structure better, the engineer must arrange the sides from longest to shortest. Which is the correct order?

Mount Purro Nature Reserve is a camping site near Pasay City. Mark and his friends are setting up a triangular tent for their camping trip. The tent's base measures 8 feet, and one of the slanted sides is 5 feet. They need to determine the possible length(s) for the other slanted side to ensure the tent forms a valid triangle. What is the range of possible values for the missing side (x) based on the Triangle Inequality Theorem?

• 3 < x < 13       

• 3 ≤ x < 13       

• 3 < x ≤ 13

• 3 < x ≤ 13