Quiz (1 point)
Given that:
quadrilateral WXYZ is convex
Prove that:
The following properties may be helpful:
- ((m∠YWX) + (m∠WXY)) + (m∠XYW) = 180
- ((m∠YWX) + (m∠WXY)) + (m∠XYW) = 180
- 180 + 180 = 360
- ((a + b) + c) + ((d + e) + f) = ((((a + b) + c) + d) + e) + f
if a = b, then a + c = b + c
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a + b = c
- d = b
then a + d = c
- if quadrilateral ABCD is convex, then point A lies in interior of ∠BCD
- if point X lies in interior of ∠ABC, then m∠ABC = (m∠ABX) + (m∠XBC)
- if quadrilateral ABCD is convex, then point C lies in interior of ∠DAB
- if point X lies in interior of ∠ABC, then m∠ABC = (m∠ABX) + (m∠XBC)
- if (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC), then (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB))
if the following are true:
- x = c + d
- y = e + f
then ((a + b) + (c + d)) + (e + f) = ((a + b) + x) + y
if ((a + b) + c) + e = ((a + b) + g) + h, then ((a + b) + c) + e = ((a + g) + b) + h
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a = b
- a = c
then b = c
Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.