Question

please explain converse of basic proportionality theorem step by step ​

Answer 1

Step-by-step explanation:

1. XPPY = XQQZ.

1. Given

2. PYXP = QZXQ

2. Taking reciprocals of both sides in statement 1.

3. PYXP + 1 = QZXQ + 1

⟹ PY+XPXP = QZ+XQXQ

⟹ XYXP = XZXQ

3. By adding 1 on both sides of statement 2.

4. In ∆XYZ and ∆XPQ,

(i) XYXP = XZXQ

(ii) ∠YXZ = ∠PXQ

4.

(i) From statement 3.

(ii) Common angle

5. Therefore, ∆XYZ ∼ ∆XPQ

5. By SAS criterion of similarity

Answer 2

Answer:

1. XPPY = XQQZ.

1. Given

2. PYXP = QZXQ

2. Taking reciprocals of both sides in statement 1.

3. PYXP + 1 = QZXQ + 1

⟹ PY+XPXP = QZ+XQXQ

⟹ XYXP = XZXQ

3. By adding 1 on both sides of statement 2.

4. In ∆XYZ and ∆XPQ,

(i) XYXP = XZXQ

(ii) ∠YXZ = ∠PXQ

4.

(i) From statement 3.

(ii) Common angle

5. Therefore, ∆XYZ ∼ ∆XPQ

5. By SAS criterion of similarity