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

Answer:

$1.\ Given$

$2.\ IV \cong VE$

$3.\ \angle GVI \cong \angle RVE$

$4.\ ASA\ congruence$

$5.\ GV \cong VR$

$6.\ Proved$

Step-by-step 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