Question
State and prove the AAS congruence postulate using the ASA congruence postulate.
The correct answer is: if any two angles and the non-included side of triangle are equal to the corresponding angles and the non-included side of the other triangle then the triangles are congruent to each other by AAS congruency rule. Hence Proved
Angle Angle Side or AAS congruence postulate – It states that if two pairs of corresponding angles along with a non-included side are equal to each other then the two triangles are said to be congruent.
Proof –
Let us consider the two triangles, ∆ABC and ∆DEF. We know
that AB = 
E, ∠B =∠E, and ∠C =∠F. We know that if two
angles of two triangles are equal then the third angle of both the triangle is equal since the sum of angles of a triangle is
Hence,
------ (1)
------ (2)
From (1) and (2) we get,
In both the triangles we know that,
Therefore, acc. to the ASA congruence rule, ∆ABC ≅ ∆DEF.
Therefore, acc. to the ASA congruence rule, 
.
Hence, if any two angles and the non-included side of triangle are equal to the corresponding angles and the non-included side of the other triangle then the triangles are congruent to each other by AAS congruency rule.
Hence Proved
Related Questions to study
Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?
Solve 0.9x+5.1x - 7 =2(2.5x - 3). How many solutions does the equation have ?
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.
Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.
Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.
¶Types of Expression
1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.
¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.
