Geometry Big Ideas chapter 1

Front

What is the equation to set up when solving for angles in a triangle?

Back

The sum of the angles in a triangle is 180 degrees, so the equation can be set up as: angle1 + angle2 + angle3 = 180.

Front

What is the definition of a midpoint in geometry?

Back

The midpoint of a line segment is the point that divides the segment into two equal parts.

Front

How do you calculate the distance between two points in a coordinate plane?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula for finding the midpoint between two points (x1, y1) and (x2, y2)?

Back

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If a point M is the midpoint of segment ST, and S is at (-5, -9), how do you find the coordinates of T?

Back

Use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2) and solve for T.

Front

What is the Pythagorean theorem and how is it used in geometry?

Back

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse.

Front

In a coordinate plane, how do you determine if a point lies on a line segment?

Back

Check if the point's coordinates satisfy the equation of the line segment.

Front

What is the significance of the coordinates of a midpoint in geometry?

Back

The coordinates of the midpoint represent the average of the endpoints' coordinates, indicating the center point of the segment.

Front

How can you apply the concept of distance in real-world problems?

Back

Distance can be used to calculate how far apart two locations are, such as in navigation or urban planning.

Front

What is the relationship between the lengths of the sides of a triangle and the angles opposite those sides?

Back

In a triangle, the larger the angle, the longer the side opposite that angle.