TRIANGLE CONGRUENCE AND SIMILARITY WORKSHEET
About "Triangle Congruence and Similarity Worksheet"
Triangle Congruence and Similarity Worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on triangle congruence and similarity.
Before look at the worksheet, if you would like to know the stuff related to triangle congruence and similarity,
Triangle Congruence and Similarity Worksheet - Problems
Problem 1 :
Check whether two triangles PQR and WXY are congruent.
Problem 2 :
Check whether two triangles PQR and JKL are congruent.
Problem 3 :
Check whether two triangles PQR and ABC are congruent.
Problem 4 :
Check whether two triangles PQR and CDE are congruent.
Problem 5 :
Check whether two triangles PQR and STU are congruent.
Problem 6 :
Check whether two triangles PQR and RST are congruent.
Problem 7 :
Check whether two triangles ABC and DEF are similar.
Problem 8 :
Determine whether the two triangles given below are similar. Justify your answer.
Problem 9 :
For what value of x is triangle ABC similar to triangle DEF.
Problem 10 :
In the diagram given below, if AC and DE are parallel, find the value of h.
Triangle Congruence and Similarity Worksheet - Solutions
Problem 1 :
Check whether two triangles PQR and WXY are congruent.
Solution :
(i) Triangle PQR and triangle WXY are right triangles. Because they both have a right angle.
(i) PQ = XY (Hypotenuse).
(ii) PR = WX (Leg)
Hence, the two triangles PQR and WXY are congruent by Hypotenuse-Leg theorem.
Problem 2 :
Check whether two triangles PQR and JKL are congruent.
Solution :
(i) PR = LK (Given)
(ii) ∠R = ∠K (Given)
(i) RQ = JK (Given)
Hence, the two triangles PQR and JKL are congruent by SAS postulate.
Problem 3 :
Check whether two triangles PQR and ABC are congruent.
Solution :
(i) PQ = BC (Hypotenuse)
(ii) ∠Q = ∠B (Acute angle)
Hence, the two triangles PQR and ABC are congruent by Hypotenuse-Acute Angle theorem.
Problem 4 :
Check whether two triangles PQR and CDE are congruent.
Solution :
(i) ∠R = ∠D (Given)
(ii) PR = ED (Given)
(iii) ∠P = ∠E (Given)
Hence, the two triangles PQR and CDE are congruent by ASA postulate.
Problem 5 :
Check whether two triangles PQR and STU are congruent.
Solution :
(i) PQ = ST (Given)
(ii) PR = SU (Given)
(iii) QR = TU (Given)
Hence, the two triangles PQR and STU are congruent by SSS postulate.
Problem 6 :
Check whether two triangles PQR and RST are congruent.
Solution :
(i) PR = RT (Given)
(ii) ∠SRT = ∠PRQ (Vertical Angles)
(iii) QR = RS (Given)
Hence, the two triangles PQR and RST are congruent by SAS postulate.
Problem 7 :
Check whether two triangles ABC and DEF are similar.
Solution :
By Triangle Sum Theorem, in Δ ABC,
∠A + ∠B + ∠C = 180°
21° + 105° + ∠C = 180°
126° + ∠C = 180°
Subtract 126° from both sides.
∠C = 54°
In triangles ABC and DEF, we have
∠A = ∠F = 21°
∠E = ∠C = 54°
Two angles of one triangle are congruent to two angles of another triangle.
By Third Angle Theorem, the third pair of angles must also be congruent.
That is,
∠B = ∠D = 105°
Hence, the triangles ABC and DEF are similar triangles.
Problem 8 :
Determine whether the two triangles given below are similar. Justify your answer.
Solution :
By Triangle Sum Theorem, in Δ ABC,
∠A + ∠B + ∠C = 180°
60° + ∠B + 79° = 180°
∠B + 139° = 180°
Subtract 139° from both sides.
∠B = 41°
By Triangle Sum Theorem, in Δ DEF,
∠D + ∠E + ∠F = 180°
60° + 42° + ∠F = 180°
102° + ∠F = 180°
Subtract 102° from both sides.
∠F = 78°
In triangles ABC and DEF, we have
∠A = ∠D = 60°
And no more pairs of angles are not congruent.
Hence, the triangles ABC and DEF are not similar triangles.
Problem 9 :
For what value of x is triangle ABC similar to triangle DEF.
Solution :
Let us assume the given two triangles are similar.
So, the ratio of the corresponding sides must be equal.
By taking the vertices of the triangle in the order (given) ABC and DEF, we have
AB / DE = BC / EF
36 / x = 30 / 15
Take reciprocal on both sides.
x / 36 = 15 / 30
x / 36 = 1 / 2
Multiply both sides by 36
x = 1/2 ⋅ 36
x = 18
Hence the two triangles ABC and DEF are similar for the value of x is 18.
Problem 10 :
In the diagram given below, if AC and DE are parallel, find the value of h.
Solution :
In the above diagram, we can consider two triangles ABC and DBE.
Given : AC and DE are parallel.
The parallel sides AC and DE are cut by the transversal EC.
Then ∠E and ∠C are corresponding angles.
When two parallel lines cut by a transversal, the corresponding angles are congruent.
So, ∠E and ∠C are congruent.
In triangles ABC and DBE, we have
∠E = ∠C
∠B is common angle
Two angles of one triangle are congruent to two angles of another triangle.
By Third Angle Theorem, the third pair of angles must also be congruent.
So, the triangles ABC and DBE are similar triangles.
In similar triangles, the ratio of the corresponding sides are equal.
Then, we have
AB / DB = BC / BE
Plug AB = h, DB = 6, BE = 16 and BC = 56.
h / 6 = 56 / 16
Multiply both sides by 6.
h = 56/16 ⋅ 6
h = 21
Hence, the value of h is 21.
After having gone through the stuff given above, we hope that the students would have understood "Triangle congruence and similarity worksheet".
Apart from the stuff given on "Triangle congruence and similarity worksheet", if you need any other stuff, 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
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
