Unit 4 Practice Test : Prove Triangles are Congruent

If B is the midpoint of AC, then AB ≅ BC.

• Definition of Congruent Segments

• Definition of Midpoint

• Vertical Angles Theorem

• Definition of Angle Bisector

Answer explanation

The correct choice is the Definition of Midpoint, which states that if B is the midpoint of AC, then AB is congruent to BC (AB ≅ BC). This directly supports the statement in the question.

Tags

CCSS.HSG.GPE.B.6

If DB bisects ∠ABC, then ∠ABD = ∠CBD.

• Definition of Congruent Angles

• Definition of Angle Bisector

• Angle Addition Postulate

• Definition of Right Angle

Answer explanation

The statement "DB bisects ∠ABC" means that DB divides ∠ABC into two equal parts. Therefore, by the definition of an angle bisector, ∠ABD = ∠CBD, making "Definition of Angle Bisector" the correct choice.

Tags

CCSS.HSG.SRT.B.5

What reasons supports the statement?

• Symmetry Property

• Reflexive Property

• Transitive Property

• SSS

Answer explanation

The Reflexive Property states that any quantity is equal to itself, supporting the statement by confirming that if a = a, then the relationship holds true. This property is fundamental in establishing equality.

Tags

CCSS.HSG.SRT.B.5

What reason supports the statement?

• Vertical angles are congruent.

• Parallel implies alternate interior angles are congruent.

• Parallel implies corresponding angles are congruent.

• Reflexive Property

Answer explanation

Vertical angles are congruent is the correct choice because it directly states a fundamental property of angles formed by intersecting lines, supporting the statement effectively.

Tags

CCSS.8.G.A.5

What reason supports the statement?

• Alternate interior angles of parallel lines are Congruent

• Definition of Angle Bisector

• Vertical angles are congruent.

• Reflexive Property

Answer explanation

The correct choice, 'Parallel implies alternate interior angles are congruent,' is based on the property of parallel lines cut by a transversal, which establishes that alternate interior angles are equal.

Tags

CCSS.8.G.A.5

Reason?

• Definition of Angle Bisector

• Vertical Angles are congruent

• Right angles are congruent

• Definition of Perpendicular Lines

Answer explanation

The correct choice is the Definition of Angle Bisector, as it specifically describes a line that divides an angle into two equal parts, which is essential for understanding angle relationships in geometry.

Tags

CCSS.HSG.CO.C.9

Reason?

• Definition of Midpoint

• Definition of Segment Bisector

• Reflexive Property

• Definition of Perpendicular Lines

Answer explanation

The Midpoint Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. This theorem is essential in proving relationships in geometric figures.

Tags

CCSS.HSG.CO.C.10

Which statement is true about the diagram?

• K is the midpoint of AB.

• B is the midpoint of KT.

• AK = BT

• AB = KT

Answer explanation

K is the midpoint of AB, meaning AK = KB. This makes the statement true. The other options do not provide correct relationships based on the diagram.

Tags

CCSS.HSG.CO.C.10

Given that BA bisects ∠DBC, which statement must be true?

• m∠ABD = m∠ABC

• AB ≅ BC

• B is the midpoint of DC.

• m∠DBC = 90°

Answer explanation

Since BA bisects ∠DBC, it means that m∠ABD = m∠ABC. This is a property of angle bisectors, making the first statement true. The other options do not necessarily follow from the given information.

Tags

CCSS.HSG.CO.C.9

Which reasoning could you use to support your statement?

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Tags

CCSS.HSG.SRT.B.5