Distance and Triangle Concepts in Geometry

The lesson covers finding distances in the coordinate plane using various activities. It includes ordering coordinate pairs by distance, calculating distances using the Pythagorean theorem, and an optional challenge on perimeter calculation. The lesson concludes with homework instructions and a summary.

What is the first step in finding the distance between two points with the same x-value?

• Subtract the y-values

• Add the x-values

• Multiply the coordinates

• Divide the y-values

If two points share the same y-value, how do you calculate the distance between them?

• Multiply the x-values

• Add the y-values

• Divide the x-values

• Subtract the x-values

Which theorem is used to find the distance between two points that do not share x or y values?

• Fundamental Theorem of Calculus

• Pythagorean Theorem

• Binomial Theorem

• Remainder Theorem

What is the hypotenuse in a right triangle?

• The longest side

• The shortest side

• The side opposite the smallest angle

• The side adjacent to the right angle

How can you identify a 3-4-5 triangle?

• By checking if the sides are multiples of 3, 4, and 5

• By ensuring all angles are 60 degrees

• By confirming all sides are equal

• By checking if the sides are multiples of 2, 3, and 4

What is the perimeter of a triangle with sides 6, 8, and 10?

• 24

• 20

• 18

• 30

What is the main concept used to find distances on the coordinate plane?

• Geometric Transformations

• Pythagorean Theorem

• Algebraic Expressions

• Trigonometric Ratios

What should you do first when finding the distance between two points on a coordinate plane?

• Find the slope

• Calculate the midpoint

• Form a right triangle

• Determine the area

What is the slope of a line that rises 8 units and runs 5 units?

• 1.6

• 0.625

• 1.25

• 2.0

What is the equation of a line with a slope of 2 and a y-intercept of 1.5?

• y = 1.5x - 2

• y = 2x + 1.5

• y = 1.5x + 2

• y = 2x - 1.5