Module2 Topic1

Benjamin, Avery, and Henry are working on a construction project for their geometry class. They have a diagram to follow. Which construction is their diagram most likely modeling?

• Angle bisector

• Duplication of an angle

• Midpoint

• Perpendicular bisector

Answer explanation

Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts. If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.

Which of the following could NOT be the lengths of the three sides of a triangle?

• 3 inches, 4 inches, 5 inches

• 5 centimeters, 12 centimeters,

  13 centimeters

• 4 yards, 6 yards, 8 yards

• 3 millimeters, 6 millimeters,

  9 millimeters

Answer explanation

Since the given sides are 3, 6, and 9.

3 + 6 is not greater than 9.

Scarlett is learning about basic geometric terms in her math class. Which of the following is NOT an undefined term?

• Point

• Line

• Plane

• Angle

Answer explanation

There are form foundational terms considered undefined in geometry. These are the point, the line, the plane, and the set

Elijah, Daniel, and Mason are discussing shapes in their geometry class. Elijah makes a statement: "All quadrilaterals with four right angles have congruent sides." Daniel disagrees and wants to give a counterexample to prove Elijah's statement is false. Which shape should Daniel use as a counterexample?

• Rectangle

• Rhombus

• Square

• Circle

Answer explanation

Counterexample is an example that makes a definition or conjecture incorrect.

Rectangle is defined as a quarilateral with opposite sides are equal

What conjecture can you make about the number of sides and the number of diagonals that can be drawn from a single vertex?

• The number of diagonals drawn from a single vertex of a polygon is equal to the number of sides of the polygon minus 3

• The number of diagonals drawn from a single vertex of a polygon is equal to the number of sides of the polygon plus 3

• The number of diagonals drawn from a single vertex of a polygon is proportional to the number of sides of the polygon.

Write the converse of the conjecture.

“If the endpoints of an arc are the same points as the points where an inscribed angle intercepts a circle, then its measure is twice that of the angle.”

Converse statement:

"If the measure of an arc is twice the measure of an inscribed angle, then its endpoints

are the same as the points where the inscribed angle intercepts the circle."

Is the converse true? If yes, write the biconditional statement. If not, write your FULL NAME

Answer explanation

A biconditional statement is a statement of the form “p, if and only if q.” This is denoted p ↔ q, and is sometimes abbreviated “p iff q.” Definition: A biconditional statement can be done if both conditional statement and converse statement are TRUE.

What additional information would have to be true for the parallelogram to also be a rhombus?

• at least 2 sides must be congruent

• all four sides are congruent

• no additional information needed

Zoe, Benjamin, and Avery are planning a road trip. They are looking at a map and trying to determine the angle between Route A and Route B at the intersection near their starting point. Determine the value of x, which represents this angle on the map.

• 115 degrees

• 35 degrees

• 180 degrees

• 80 degrees

Determine whether it is possible to form a triangle using a set of segments with the given measurements.

3, 4, and 5​

• YES. Because 5 + 4 > 3

• YES. Because 3 + 4 > 5

• NO. Because 5 -4 < 3