Two <u>lines</u> are said to be <em>parallel</em> if and only if the value of the <u>angle</u> between them is .
Thus the required proofs for each <u>question</u> are stated below:
6. A <em>bisector</em> is a line that <u>divides</u> a given line or angle into <em>two equal</em> parts.
Thus to prove that: AD ║BC
Given that: AC ⊥ BD, then:
BX ≅ DX (<em>midpoint</em> property of a <u>line</u>)
<ADX ≅ <DBX (<u>alternate</u> angle property)
<DAX ≅ <BCX (<em>alternate</em> angle property)
<AXD ≅ <BXC (<em>vertical opposite</em> angle property)
Also,
ΔAXD ≅ ΔBXC (<em>congruent</em> property of <u>similar</u> triangles)
Therefore, it can be deduced that;
AD ║BC
7. Given: CD ≅ CE
<B ≅ <D
proof: AB ║DE
<ABC ≅EDC
Thus,
CB ≅ CA (<u>congruent</u> property of similar triangle)
<BAC ≅ <EDC (<em>alternate</em> angle property)
ABC ≅ <DEC (<em>alternate</em> angle property)
Also,
CA ≅ CB <u>(congruent </u>side of <em>similar </em>triangles)
ΔABc ≅ ΔCDE (<em>congruent</em> property of <u>similar</u> triangles)
Thus,
AB ║DE (<u>congruent</u> property)
8. Prove: AB ║ DE
Given: <1 ≅ < 3
Then,
<1 ≅ <2 ≅ <3 ≅
So that,
BC ≅ EF
also,
<1 + <2 = (<em>supplementary </em>angles)
Therefore it can be inferred that;
AB ║ DE (<em>congruent</em> property of <u>parallel</u> lines intersected by <em>transversals</em>)
For more clarifications on parallel lines, visit: brainly.com/question/24607467
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