Question

Can someone help me out on these geometry questions? ASAP!!!

Write formal proofs the LL Theorm.

Answer 1

Question 6

1)
`\overline{AB} \cong \overline{BD}`,
`\overline{CD} \perp \overline{BD}`, O is the midpoint of
`\overline{BD}`,
`\overline{AB} \cong \overline{CD}` (given)

2)
`\angle ABO, \angle ODC` are right angles (perpendicular lines form right angles)

3)
`\triangle ABO, \triangle CDO` are right triangles (a triangle with a right angle is a right triangle)

4)
`\overline{BO} \cong \overline{OD}` (a midpoint splits a segment into two congruent parts)

5)
`\triangle ABO \cong \triangle CDO` (LL)

Question 7

1)
`\angle ADC, \angle BDC` are right angles),
`\overline{AD} \cong \overline{BD}`

2)
`\overline{CD} \cong \overline{CD}` (reflexive property)

3)
`\triangle CDA, \triangle CDB` are right triangles (a triangle with a right angle is a right triangle)

4)
`\triangle ADC \cong \triangle BDC` (LL)

5)
`\overline{AC} \cong \overline{BC}` (CPCTC)

Question 8

1)
`\overline{CD} \perp \overline{AB}`, point D bisects
`\overline{AB}` (given)

2)
`\angle CDA, \angle CDB` are right angles (perpendicular lines form right angles)

3)
`\triangle CDA, \triangle CDB` are right triangles (a triangle with a right angle is a right triangle)

4)
`\overline{AD} \cong \overline{DB}` (definition of a bisector)

5)
`\overline{CD} \cong \overline{CD}` (reflexive property)

6)
`\triangle ADC \cong \triangle BDC` (LL)

7)
`\angle ACD \cong \angle BCD` (CPCTC)