Cycle 2 Day 1 Mathematics 10

Multiple Choice

According to Theorem 3.2, what is the significance of the perpendicular segment from the center to a chord in a circle?

• It bisects the chord.

• It is always the longest segment in the circle.

• It passes through the midpoint of the circle.

• It is equal to the radius of the circle.

Open Ended

Explain why a segment from the center of a circle that is perpendicular to a chord becomes a perpendicular bisector of that chord.

Multiple Choice

According to Theorem 3.2, what is the relationship between congruent chords and their distance from the center of a circle?

• Congruent chords are equidistant from the center

• Congruent chords are closer to the circumference

• Congruent chords are always perpendicular to the radius

• Congruent chords are equal in length but not equidistant

Multiple Choice

In Circle O, if AB and CD are congruent chords, which of the following statements must be true?

• OX = OY

• OX > OY

• OX < OY

• OX + OY = radius

Multiple Choice

Find the value of x.

• 10
• 5
• 18
• 9

Multiple Choice

Which of the following statements is a direct consequence of Theorem 3.2B?

• Chords equidistant from the center are congruent

• Chords perpendicular to the radius are always equal

• All chords in a circle are congruent

• Chords passing through the center are always the longest

Multiple Choice

According to Theorem 3.2B, if the distances from the center to two chords in a circle are equal, what can be said about the chords?

• The chords are congruent.

• The chords are perpendicular.

• The chords are parallel.

• The chords are bisected by the center.

Multiple Choice

Why can't we conclude that AB = ED even if AC = FD in the given circle diagram?

• Because AB and ED are not necessarily congruent if AC and FD are congruent.

• Because AB and ED are diameters.

• Because AB and ED are radii.

• Because AB and ED are perpendicular.

Multiple Choice

Find the value of x.

• 10
• 181
• 34
• 40

Multiple Choice

Which of the following statements about perpendicular lines and bisectors is correct?

• Perpendicular lines form a right angle and bisectors divide a segment into two congruent parts.

• Perpendicular lines divide a segment into two congruent parts.

• Bisectors form a right angle.

• Perpendicular lines and bisectors are always parallel.

Open Ended

Explain how the concept of congruent arcs relates to congruent chords in a circle. Use theorems discussed in the lesson to support your answer.

Multiple Choice

If two chords in a circle are congruent, what does Theorem 3.3 state about their corresponding arcs?

• Their corresponding arcs are also congruent.

• Their corresponding arcs are bisected.

• Their corresponding arcs are perpendicular.

• Their corresponding arcs are equal to the diameter.

Multiple Choice

Which theorem states that if two chords of a circle are congruent, then their corresponding arcs are also congruent?

• Theorem 3.1

• Theorem 3.2

• Theorem 3.3

• Theorem 3.4

Multiple Choice

Given that FG ≅ HJ and mFG = 70, what is the value of x in the circle shown?

• 70

• 35

• 140

• 90

Fill in the Blanks

Multiple Choice

What is the length of segment RS?

• 24

• 42

• 82

• 28

Multiple Select

Which of the following statements are true about radii and chords in a circle?

• All radii in a circle have the same length.

• Congruent chords have congruent arcs.

• The sum of the angles in a triangle is 180 degrees.

• All chords in a circle are equal.