Question

Every proof needs Given and Prove statements. Use the endpoints on the diagram to write a Given statement indicating the down tube is longer than the top tube. Prove the relationship between the opposite angles of the given sides. (2 points; 1 point for the Given statement, 1 point for the Prove statement)

Answer 1

m<ABC > m<ACB (angle property of a triangle)

Explanation:

Given that: ΔABC

AB = AX

Prove: m<ABC > m<ACB

From the given diagram,

ΔABX is an isosceles triangle (two congruent sides and angles)

<AXB = m<ABX =
`90^(o)` (isosceles triangle property)

AC = AX + XC

Thus,

AC > AB

m<ABC = m1 + m3 ≥
`90^(o)`

m<ACB <
`90^(o)` (acute angle property)

Therefore since in a triangle the longest side is opposite to the greatest angle, then;

m<ABC > m<ACB (angle property of a triangle)