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USPshnik [31]
2 years ago
9

What is the reason for statement 5 in this proof?

Mathematics
3 answers:
Sloan [31]2 years ago
5 0

You are comparing side AB, angle ABD, and side BD in one triangle to side CB, angle CBD, and side BD in the other triangle. That is, you are comparing a Side, Angle, and Side in each triangle. The SAS postulate is the reason the triangles are congruent.

kondor19780726 [428]2 years ago
4 0

Answer:

The correct option is D) SAS

Step-by-step explanation:

Consider the provided statement.

SAS Similarity Theorem: If two sides of a triangle are proportional to the two sides of another triangle and the included angle in both are congruent, then the two triangles are similar.

Statement 1: Let ΔABC be an isosceles triangle where AB = BC.

Reason 1: Given

Statement 2: Create point D on so that bisects ∠ABC as shown.

Reason 2: Constructing an angle bisector.

Statement 3: m∠ABD = m∠DBC

Reason 3: Definition of angle bisector

Statement 4: BD = BD

Reason 4: Reflexive Property of Equality

Statement 5: ΔABD ≅ ΔCBD

Reason 5: SAS

Statement 6: m∠BAC = m∠BCA

Reason 6: Corresponding angles of congruent triangles are equal.

From Reflexive Property of Equality we know BD=BD, m∠ABD = m∠DBC definition of angle bisector and AB = BC, which follows the Side angle side (SAS) similarity.

Gavion2 years ago
0 0

What is the reason for statement 5 in this proof?

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