Quiz (1 point)
Given that:
△ABC ∼ △XYZ
M is the midpoint of line AC
N is the midpoint of line XZ
Prove that:
The following properties may be helpful:
- (a ⋅ 2) / (b ⋅ 2) = a / b
- if △ABC ∼ △DEF, then m∠BCA = m∠EFD
- if △ABC ∼ △DEF, then (distance CA) / (distance FD) = (distance BC) / (distance EF)
- if M is the midpoint of line AB, then (distance BM) ⋅ 2 = distance BA
- if M is the midpoint of line AB, then (distance BM) ⋅ 2 = distance BA
if the following are true:
- a = x
- b = y
then a / b = x / y
if the following are true:
- a = b
- a = c
then b = c
if the following are true:
- a = b
- b = c
then a = c
if a = b, then b = a
- if M is the midpoint of line AB, then m∠AMB = 180
- if M is the midpoint of line AB, then m∠AMB = 180
- if (m∠ABC = 180) and (m∠IJK = 180) and (m∠XCA = m∠YKI), then m∠XCB = m∠YKJ
- if (m∠ABC = m∠XYZ) and ((distance AB) / (distance XY) = (distance BC) / (distance YZ)), then △ABC ∼ △XYZ
- if △ABC ∼ △DEF, then (distance AC) / (distance DF) = (distance AB) / (distance DE)
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.