G8-Q4-Csilvestre

The Triangle Challenge

 

Lena and David are working on a geometry project for their school’s math competition. Their task is to design a triangular park and ensure the side lengths meet specific conditions.

Lena has already chosen two of the sides of the park to be 7 meters and 9 meters long. Now, she needs to determine the possible length for the third side, so she turns to David for help. To help her, David remembers the Triangle Inequality Theorem, which says that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

After some calculations, they realize they need to check whether the chosen side lengths follow this rule and what the possible range for the third side could be.

Given that Lena has chosen two sides of the triangle to be 7 meters and 9 meters, which of the following could NOT be the length of the third side?

 

• 3 meters

• 5 meters

• 10 meters

• 16 meters

The Triangle Challenge

 

Lena and David are working on a geometry project for their school’s math competition. Their task is to design a triangular park and ensure the side lengths meet specific conditions.

Lena has already chosen two of the sides of the park to be 7 meters and 9 meters long. Now, she needs to determine the possible length for the third side, so she turns to David for help. To help her, David remembers the Triangle Inequality Theorem, which says that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

After some calculations, they realize they need to check whether the chosen side lengths follow this rule and what the possible range for the third side could be.

If Lena wants to maximize the area of the triangular park, what strategy should she use to determine the length of the third side?

• Choose the largest possible length for the third side.

• Choose the smallest possible length for the third side.

• Choose a length that is close to the average of the other two sides

• Use a formula that directly calculates the area of a triangle given two sides and

       the included angle

THE INTERSECTING ROADS

 

In a small town, there are two roads that run side by side, going in the same direction. These two roads are parallel roads because they never meet, no matter how far they stretch. A new road, called Tran Road, is being built and it cuts across both parallel roads at an angle.

When Tran Road crosses the parallel roads, it creates several angles. The engineers in the town want to figure out certain rules about these angles to make sure the roads are built correctly. Specifically, they want to prove that some angles formed by Tran Road and the parallel roads are always the same.

 

The engineers notice that the angle between Tran Road and the first parallel road is 135°. They want to find out what the angle between Tran Road and the second parallel road will be.

What is the measure of this corresponding angle between Tran Road and the second parallel road?

• 135°

• 145°

• 55°

• 70°

THE INTERSECTING ROADS

 

In a small town, there are two roads that run side by side, going in the same direction. These two roads are parallel roads because they never meet, no matter how far they stretch. A new road, called Tran Road, is being built and it cuts across both parallel roads at an angle.

When Tran Road crosses the parallel roads, it creates several angles. The engineers in the town want to figure out certain rules about these angles to make sure the roads are built correctly. Specifically, they want to prove that some angles formed by Tran Road and the parallel roads are always the same.

 

When Tran Road intersects the two parallel roads, which pairs of angles will always be congruent?

• Corresponding angles

• Alternate interior angles

• Alternate exterior angles

• All of the above

THE INTERSECTING ROADS

 

In a small town, there are two roads that run side by side, going in the same direction. These two roads are parallel roads because they never meet, no matter how far they stretch. A new road, called Tran Road, is being built and it cuts across both parallel roads at an angle.

When Tran Road crosses the parallel roads, it creates several angles. The engineers in the town want to figure out certain rules about these angles to make sure the roads are built correctly. Specifically, they want to prove that some angles formed by Tran Road and the parallel roads are always the same.

 

Alex is studying the angles formed by Tran Road and the two parallel roads. If he knows the measure of one angle, how can he determine the measures of the other angles formed by the intersection of Tran Road and the parallel lines?

• By using a protractor to measure each angle individually.

• By applying the properties of parallel lines and transversal lines to identify

      congruent and supplementary angles.

• By using a formula that calculates the measure of an angle based on the lengths of

       the sides of the triangle formed by Tran Road and the parallel lines.

• By measuring the lengths of the sides of the triangles formed by Tran Road and the

       parallel lines and using trigonometric ratios.

   

You're a furniture designer working at a local shop in the Philippines. One day, your supervisor tasked you with designing a wooden shoe rack for a renowned film industry artist in Thailand. The piece will be exported, so it needs to be durable, stylish, and shippable. Eager to impress your boss and represent Philippine craftsmanship, you immediately set to work, researching various design ideas online.

 

Below is your design:

• Lines that intersect at exactly one point, like the crossbars of a goalpost.

• Lines that are always the same distance apart and never meet, such as the

        opposite sides of a rectangle.

• Lines that form a right angle, like the adjacent sides of a square.

• Lines that slant in opposite directions, like the diagonals of a rhombus.

   

You're a furniture designer working at a local shop in the Philippines. One day, your supervisor tasked you with designing a wooden shoe rack for a renowned film industry artist in Thailand. The piece will be exported, so it needs to be durable, stylish, and shippable. Eager to impress your boss and represent Philippine craftsmanship, you immediately set to work, researching various design ideas online.

 

Below is your design:

Why is it important to ensure that certain parts of a shoe rack design have parallel lines?

• Parallel lines make the design look more trendy and modern.

• Parallel lines are easier to measure and cut during the construction process.

• Parallel lines provide structural stability and balance to the design, preventing the    

       shoe rack from wobbling or tipping over.

• Parallel lines are a common design element in furniture, and using them can

        make the shoe rack look more traditional.

   

You're a furniture designer working at a local shop in the Philippines. One day, your supervisor tasked you with designing a wooden shoe rack for a renowned film industry artist in Thailand. The piece will be exported, so it needs to be durable, stylish, and shippable. Eager to impress your boss and represent Philippine craftsmanship, you immediately set to work, researching various design ideas online.

 

Below is your design:

If you were to design a shoe rack with a slanted top, how could you use the concept of parallel lines to maintain stability and visual appeal?

• By avoiding the use of parallel lines in the design, as they may clash with the

        slanted top.

• By making all the shelves slanted to match the top, creating a dynamic and

        unconventional design.

• By using curved lines instead of straight lines, to soften the overall look of the

        shoe rack.

• By using vertical supports that are parallel to each other, providing stability and

        creating a visually pleasing contrast with the slanted top.

THE DICE DECIDES

 

Fe and Haydee were about to start a game of Scrabble but needed to decide who would go first. Fe suggested they roll a six-sided die to make it fair. Haydee rolled first and landed on a 4, then Fe rolled a 2, so it was decided—Haydee would go first. They laughed, knowing the die had made the choice, but the real challenge would be in the words they played!

What is the experiment in this scenario?

• Playing a game of Scrabble.

• Rolling a six-sided die.

• Choosing who goes first in Scrabble.

• Playing a word game.

THE DICE DECIDES

 

Fe and Haydee were about to start a game of Scrabble but needed to decide who would go first. Fe suggested they roll a six-sided die to make it fair. Haydee rolled first and landed on a 4, then Fe rolled a 2, so it was decided—Haydee would go first. They laughed, knowing the die had made the choice, but the real challenge would be in the words they played!

How does rolling the die help ensure fairness in determining who goes first in the game?

• It guarantees that each player has an equal chance of going first.

• It eliminates any potential arguments or disagreements between the players.

• It adds an element of chance and excitement to the game's beginning.

• All of the above.