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)