Question

Can someone help me with these 4 geometry questions? Pls it’s urgent, So ASAP!!!!

Answer 1

Question 4

1)
`\overline{BD}` bisects
`\angle ABC`,
`\overline{EF} \perp \overline{AB}`, and
`\overline{EG} \perp \overline{BC}` (given)

2)
`\angle FBE \cong \angle GBE` (an angle bisector splits an angle into two congruent parts)

3)
`\angle BFE` and
`\angle BGE` are right angles (perpendicular lines form right angles)

4)
`\triangle BFE` and
`\triangle BGE` are right triangles (a triangle with a right angle is a right triangle)

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

6)
`\triangle BFE \cong \triangle BGE` (HA)

Question 5

1)
`\angle AXO` and
`\angle BYO` are right angles,
`\angle A \cong \angle B`,
`O` is the midpoint of
`\overline{AB}` (given)

2)
`\triangle AXO` and
`\triangle BYO` are right triangles (a triangle with a right angle is a right triangle)

3)
`\overline{AO} \cong \overline{OB}` (a midpoint splits a segment into two congruent parts)

4)
`\triangle AXO \cong \triangle BYO` (HA)

5)
`\overline{OX} \cong \overline{OY}` (CPCTC)

Question 6

1)
`\angle B` and
`\angle D` are right angles,
`\overline{AC}` bisects
`\angle BAD` (given)

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

3)
`\angle BAC \cong \angle CAD` (an angle bisector splits an angle into two congruent parts)

4)
`\triangle BAC` and
`\triangle CAD` are right triangles (a triangle with a right angle is a right triangle)

5)
`\triangle BAC \cong \triangle DCA` (HA)

6)
`\angle BCA \cong \angle DCA` (CPCTC)

7)
`\overline{CA}` bisects
`\angle ACD` (if a segment splits an angle into two congruent parts, it is an angle bisector)

Question 7

1)
`\angle B` and
`\angle C` are right angles,
`\angle 4 \cong \angle 1` (given)

2)
`\triangle BAD` and
`\triangle CAD` are right triangles (definition of a right triangle)

3)
`\angle 1 \cong \angle 3` (vertical angles are congruent)

4)
`\angle 4 \cong \angle 3` (transitive property of congruence)

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

6)
`\therefore \triangle BAD \cong \triangle CAD` (HA theorem)

7)
`\angle BDA \cong \angle CDA` (CPCTC)

8)
`\therefore \vec{DA}` bisects
`\angle BDC` (definition of bisector of an angle)