Question

Activity 2 Direction: Complete the proof. Given: V is the midpoint of |E, angle| cong angle E Prove: V is the midpoint of GR Proof: Statements 1. V is the midpoint of IE, 21 2. 3. 4. AGVI ARVE 5. 6. V is the midpoint of GR Q3 Week No.9 Competency E R Reasons Definition of Midpoint E 1. 2. 3. Vertical Angle Theorem 5. CPCTC 6. 5 Code: M8GE-Illh-1, M8GE-Illi-j-1 Activity 3 Direction: Fill in the missing statements and reasons. Given: GA bisects angle G; overline GA perp L overline D Prove: overline GL cong overline GD Proof: Statements 1. GA bisects 4G 2 . 3 . 4. ZGAL and angle GAD are right angles 5 . 6. overline GA cong overline GA; 7. Delta GAL cong Delta GAD; 8. overline GL cong overline GD L D Reasons Bisector 1. 2. Definition of Angle 3. Given 4 . 5. All right angles are congruent. 6. 7 . 8.​

Answer 1

`1.\ Given`

`2.\ IV \cong VE`

`3.\ \angle GVI \cong \angle RVE`

`4.\ ASA\ congruence`

`5.\ GV \cong VR`

`6.\ Proved`

Explanation:

Given

See attachment for right question format

Required

Complete the blanks

1. V is the
`midpoint` of |E,
`\angle I \cong \angle E` ---- This statement was stated in the question.

So, the reason is Given

2. Midpoint means halfway. So, we can fill the statement column with:

`IV \cong VE` --- because V is the midpoint of IV and VE

or
`GV \cong VR` --- because V is the midpoint of GV and VR

3. Vertical angle are congruent. So, the statement is:

`\angle GVI \cong \angle RVE` which means that angles at V are congruent

4. We have:

`\triangle GVI \cong \triangle RVE` because

`\angle GVI \cong \angle RVE` --- congruent angles (A)

`IV \cong VE` ---- congruent sides (S)

`\angle GIV \cong \angle REV` --- congruent angles (A)

The above implies that:
`\triangle GVI \cong \triangle RVE` because of ASA congruence

5. CPCTC is true here because GV and VR are corresponding sides of triangles GVI and RVE. ----
`\triangle GVI \cong \triangle RVE`

Hence, both sides are congruent ----
`GV \cong VR`

6. The given statement has been prived