Geometry

(see attached images)

The Proof and Explanation  for

Part C ,

Qs 9 and

Qs 10  are below.

Step-by-step explanation:

PART C .

Given:

AD || BC ,

To Prove:

ΔAED ≅ ΔCEB

Proof:

Statement                             Reason

1. AD || BC                           1. Given

2. ∠A ≅ ∠C                        2. Alternate Angles Theorem as AD || BC

3. ∠AED ≅ ∠CEB               3. Vertical Opposite Angle Theorem.

4. AE ≅ EC                         4. Given

5. ΔAED ≅ ΔCEB               5. By A-S-A congruence testProved

Qs 9)

Given:

AB ≅ BC ,

∠ABD ≅ ∠CBD

To Prove:

∠A ≅ ∠C

Proof:

Statement                             Reason

1. ∠ABD ≅ ∠CBD              1. Given

2. AB ≅ CB                       2. Given      

3. BD ≅ BD                       3. Reflexive Property

4. ΔABD ≅ ΔCBD             4. By S-A-S congruence test

5. ∠A ≅ ∠C                       5. Corresponding parts of congruent Triangles Proved.

Qs 10)

Given:

∠MCI ≅ ∠AIC

MC ≅ AI

To Prove:

ΔMCI ≅ ΔAIC

Proof:

Statement                             Reason

1. ∠MCI ≅ ∠AIC       1. Given

2. MC ≅ AI              2. Given

3. CI ≅ CI                3. Reflexive Property

4. ΔMCI ≅ ΔAIC     4. By S-A-S congruence test