Using Congruent Triangles Worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on using congruent triangles.
Problem 1 :
In the diagram shown below, AB  CD, BC  DA. Prove that
AB ≅ CD
Problem 2 :
In the diagram shown below,
A is the midpoint of MT
A is the midpoint of SR
Prove that MS  TR.
Problem 3 :
In the diagram shown below,
∠1 ≅ ∠2
∠3 ≅ ∠4
Prove that ΔBCE ≅ ΔDCE.
Problem 1 :
In the diagram shown below, AB  CD, BC  DA. Prove that
AB ≅ CD
Plane for Proof :
Show that ΔABD ≅ ΔCDB. Then use the fact that corresponding parts of congruent triangles are congruent.
Solution :
First copy the diagram and mark it with the given information. Then mark any additional information that we can deduce. Because AB and CD are parallel segments intersected by a transversal, BC and DA are parallel segments intersected by a transversal, we can deduce that two pairs of alternate interior angles are congruent.
Mark given information :
Add deduced information :
Paragraph Proof :
Because AB  CD, it follows from the Alternate Interior Angles Theorem, that ∠ABD ≅ ∠CDB. For the same reason, ∠ADB ≅ ∠CBD, because BC  DA. By the Reflexive Property of Congruence, BD ≅ BD. We can use the ASA congruence postulate to conclude that
ΔABD ≅ ΔCDB.
Finally, because corresponding parts of congruent triangles are congruent, it follows that
AB ≅ CD
Problem 2 :
In the diagram shown below,
A is the midpoint of MT
A is the midpoint of SR
Prove that MS  TR.
Plane for Proof :
Prove that ΔMAS ≅ ΔTAR. Then use the fact that corresponding parts of congruent triangles are congruent to show that ∠M ≅ ∠T. Because these angles are formed by two segments intersected by a transversal, we can conclude that MS  TR.
Solution :
Statements A is the midpoint of MT A is the midpoint of SR MA ≅ TA, SA ≅ RA ∠MAS ≅ ∠TAR ΔMAS ≅ ΔTAR aaaaaaaa∠M ≅ ∠Taaaaaaa aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa MS  TR

Reasons Given Given Definition of midpoint Vertical Angles Theorem SAS Congruence Postulate Corresponding parts of congruent triangles are congruent. Alternate Interior Angles Converse 
Problem 3 :
In the diagram shown below,
∠1 ≅ ∠2
∠3 ≅ ∠4
Prove that ΔBCE ≅ ΔDCE.
Plane for Proof :
The only information we have about ΔBCE and ΔDCE is that ∠1 ≅ ∠2 and that CE ≅ CE. Notice, however, that sides BC and DC are also sides of ΔABC and ΔADC. If we can prove that ΔABC ≅ ΔADC, we can use the fact that corresponding parts of congruent triangles are congruent to get a third piece of information about ΔBCE and ΔDCE.
Solution :
Statements ∠1 ≅ ∠2 ∠3 ≅ ∠4 AC ≅ AC ΔABC ≅ ΔADC BC ≅ DC CE ≅ CE ΔBCE ≅ ΔDCE 
Reasons Given Given Reflexive Property of Congruence ASA Congruence Postulate Corresponding parts of ≅ Δ are ≅ Reflexive Property of Congruence SAS Congruence Postulate 
After having gone through the stuff given above, we hope that the students would have understood, "Using congruent triangles worksheet".
Apart from the stuff given above, if you want to know more about "Using congruent triangles", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits