PROVING TRIANGLES ARE CONGRUENT WORKSHEET
About "Proving triangles are congruent worksheet"
Proving Triangles are Congruent Worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on congruent triangles.
To know about "Triangle Congruence postulates" in detail,
Proving Triangles are Congruent Worksheet - Problems
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.
Proving Triangles are Congruent Worksheet - Solution
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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