**Problem 1 : **

In the diagram given below, prove that ΔPQW ≅ ΔTSW.

**Problem 2 : **

In the diagram given below, prove that ΔABC ≅ ΔFGH.

**Problem 3 : **

In the diagram given below, prove that ΔAEB ≅ ΔDEC.

**Problem 4 : **

In the diagram given below, prove that ΔABD ≅ ΔEBC.

**Problem 5 : **

In the diagram given below, prove that ΔEFG ≅ ΔJHG.

**Problem 1 : **

In the diagram given below, prove that ΔPQW ≅ ΔTSW.

**Solution :**

PQ ≅ ST PW ≅ TW QW ≅ SW ΔPQW ≅ ΔTSW |
Given Given Given SSS Congruence Postulate |

**Problem 2 : **

In the diagram given below, prove that ΔABC ≅ ΔFGH.

**Solution :**

Because AB = 5 in triangle ABC and FG = 5 in triangle FGH,

AB ≅ FG.

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

AC ≅ FH.

Use the distance formula to find the lengths of BC and GH.

**Length of BC : **

**BC = √[(x _{2} - x_{1})^{2} + **

**Here (****x _{1}**, y

**BC = √[(-4 + 7) ^{2} + (5 - 0)^{2}]**

**BC = √[3**^{2}** + 5**^{2}**]**

**BC = √[9 + 25]**

**BC = √34**

**Length of GH : **

**GH = ****√[(x _{2} - x_{1})^{2} + **

**Here (****x _{1}**, y

**GH = √[(6 - 1****) ^{2}**

**GH = √[5**^{2}** + 3**^{2}**]**

**GH = √[25 + 9]**

**GH = √34**

**Conclusion :**

Because BC = √34 and GH = √34,

BC ≅ GH

All the three pairs of corresponding sides are congruent. By SSS congruence postulate,

ΔABC ≅ ΔFGH

**Problem 3 : **

In the diagram given below, prove that ΔAEB ≅ ΔDEC.

**Solution : **

AE ≅ DE, BE ≅ CE ∠1 ≅ ∠2 ΔAEB ≅ ΔDEC |
Given Vertical Angles Theorem SAS Congruence Postulate |

**Problem 4 : **

In the diagram given below, prove that ΔABD ≅ ΔEBC.

BD ≅ BC AD || EC ∠D ≅ ∠C ∠ABD ≅ ∠EBC ΔABD ≅ ΔEBC |
Given Given Alternate Interior Angles Theorem Vertical Angles Theorem ASA Congruence Postulate |

**Problem 5 : **

In the diagram given below, prove that ΔEFG ≅ ΔJHG.

FE ≅ JH ∠E ≅ ∠J ∠EGF ≅ ∠JGH ΔEFG ≅ ΔJHG |
Given Given Vertical Angles Theorem AAS Congruence Postulate |

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