In ΔABC shown below, is parallel to : The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

Statement

Reason

1.

1. Given

2. is a transversal that intersects two parallel lines.

2. Conclusion from Statement 1.

3.

3.

4. ∠B ≅ ∠B

4. Reflexive Property of Equality

5.

5.

6.

6. Converse of the Side-Side-Side Similarity Theorem

Which statement and reason accurately completes the proof? (5 points)

3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

3. ΔBDE ∼ ΔBAC; Corresponding Angles Postulate

5. ∠BDE ∼ ∠BAC; Angle-Angle (AA) Similarity Postulate

3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate

5. ΔBDE ∼ ΔBAC; Angle-Angle (AA) Similarity Postulate

3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate

5. ΔBDE ∼ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

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step-by-step explanation: