PROVING TRIANGLES ARE CONGRUENT WORKSHEET
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.
Detailed Answer Key
Problem 1 :
In the diagram given below, prove that ΔPQW ≅ ΔTSW.
Solution :
|
Statements PQ ≅ ST PW ≅ TW QW ≅ SW ΔPQW ≅ ΔTSW |
Reasons 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 = √[(x2 - x1)2 + (y2 - y1)2]
Here (x1, y1) = B(-7, 0) and (x2, y2) = C(-4, 5)
BC = √[(-4 + 7)2 + (5 - 0)2]
BC = √[32 + 52]
BC = √[9 + 25]
BC = √34
Length of GH :
GH = √[(x2 - x1)2 + (y2 - y1)2]
Here (x1, y1) = G(1, 2) and (x2, y2) = H(6, 5)
GH = √[(6 - 1)2 + (5 - 2)2]
GH = √[52 + 32]
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 :
|
Statements AE ≅ DE, BE ≅ CE ∠1 ≅ ∠2 ΔAEB ≅ ΔDEC |
Reasons Given Vertical Angles Theorem SAS Congruence Postulate |
Problem 4 :
In the diagram given below, prove that ΔABD ≅ ΔEBC.
|
Statements BD ≅ BC AD || EC ∠D ≅ ∠C ∠ABD ≅ ∠EBC ΔABD ≅ ΔEBC |
Reasons Given Given Alternate Interior Angles Theorem Vertical Angles Theorem ASA Congruence Postulate |
Problem 5 :
In the diagram given below, prove that ΔEFG ≅ ΔJHG.
|
Statements FE ≅ JH ∠E ≅ ∠J ∠EGF ≅ ∠JGH ΔEFG ≅ ΔJHG |
Reasons Given Given Vertical Angles Theorem AAS Congruence Postulate |
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