Given:In quadrilateral WXYZ , and bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram.

Statement

Reason

1. and bisect each other. given
2. WA = YA
XA = ZA

definition of bisection

3. m∠YAZ = m∠XAW

Vertical Angles Theorem

4.

SAS criterion for congruence

5. ∠ YWX ≅ ∠WYZ

Corresponding angles of congruent triangles are congruent.

6. ||

converse of Alternate Interior Angles Theorem

7. m∠XAY = m∠ZAW

Vertical Angles Theorem

8. ∆XAY ≅ ∆ZAW

SAS criterion for congruence

9. ∠XZW ≅ ∠ZXY

Corresponding angles of congruent triangles are congruent.

10. ||

converse of Alternate Interior Angles Theorem

11. Quadrilateral WXYZ is a
parallelogram.

definition of parallelogram

What is the missing statement in this proof?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

These graph is cross the yaxis and x axis two ways.