PROVING STATEMENTS ABOUT ANGLES WORKSHEET
About "Proving statements about angles worksheet"
Proving statements about angles worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on Properties of Angle Congruence.
Proving statements about angles worksheet - Problems
Problem 1 :
Prove the Transitive Property of Congruence for angles.
Problem 2 :
In the diagram shown below,
m∠3 = 40°, ∠1 ≅ ∠2, ∠2 ≅ ∠3
Prove m∠1 = 40°
Problem 3 :
In the diagram shown below,
∠1 and ∠2 are right angles
Prove ∠1 ≅ ∠2
Problem 4 :
In the diagram shown below,
∠1 and ∠2 are supplements,
∠3 and ∠4 are supplements,
∠1 ≅ ∠4
Prove ∠2 ≅ ∠3
Proving statements about angles worksheet - Solution
Problem 1 :
Prove the Transitive Property of Congruence for angles.
Solution :
To prove the Transitive Property of Congruence for angles, begin by drawing three congruent angles.
Label the vertices as A, B and C.
Given :
∠A ≅ ∠B
∠B ≅ ∠C
Prove :
∠A ≅ ∠C
Statements
∠A ≅ ∠B, ∠B ≅ ∠C
m∠A = m∠B
m∠B = m∠C
m∠A = m∠C
∠A ≅ ∠C
Reasons
Given
Definition of congruent angles
Definition of congruent angles
Transitive property of equality
Definition of congruent angles
Problem 2 :
In the diagram shown below,
m∠3 = 40°, ∠1 ≅ ∠2, ∠2 ≅ ∠3
Prove m∠1 = 40°
Solution :
Statements
m∠3 = 40°
∠1 ≅ ∠2
∠2 ≅ ∠3
∠1 ≅ ∠2
m∠1 = m∠3
m∠1 = 40°
Reasons
Given
Transitive Property of Congruence
Definition of congruent angles
Substitution property of equality
Problem 3 :
In the diagram shown below,
∠1 and ∠2 are right angles
Prove ∠1 ≅ ∠2
Statements
aaaa ∠1 and ∠2 are aa aaaaa right angles
m∠1 = 90°, m∠2 = 90°
m∠1 = m∠2
∠1 ≅ ∠2
Reasons
Given aaaaaaaaaaaaaaaaaaaaa aaaaaaaaa
Definition of right angle
Transitive property of equality
Definition of congruent angles
Problem 4 :
In the diagram shown below,
∠1 and ∠2 are supplements,
∠3 and ∠4 are supplements,
∠1 ≅ ∠4
Prove ∠2 ≅ ∠3
Statements
∠1 and ∠2 are supplements
∠3 and ∠4 are supplements
∠2 ≅ ∠3
m∠1 + m∠2 = 180° m∠3 + m∠4 = 180°
m∠1 = m∠4
a ∠1 + ∠2 = ∠3 + ∠1 aaaaaa
m∠2 = m∠3
∠2 ≅ ∠3
Reasons
aaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa
Given aaaaaaaaaaaaaaaaaaaaaa aaaaaa
Definition of Supplementary angles aaaaaaaaaaaaaaaaaaaa
Definition of congruent angles
Substitution property of equality aaaaaaaaaaaaaaaaaa
Subtraction property of equality
Definition of congruent angles
After having gone through the stuff given above, we hope that the students would have understood, how to prove statements about angles.
Apart from the stuff given above, if you want to know more about "Proving statements about angles", 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
