1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Brut [27]
3 years ago
5

Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congrue

nce theorem can be used to prove that the triangles are congruent?
a.SSS
b.AAS
c.SAS
d.HL

Mathematics
2 answers:
Lana71 [14]3 years ago
7 0

The correct option is \boxed{\bf option B} i.e., AAS.

Further explanation:

Given that two angles of one triangle and the non-included side are congruent to the corresponding parts of another triangle.

ASA congruence rule:

If two angles and the included side of one triangle are congruent to two angles and the included side of other triangle, then both the triangles are congruent from the Angle-Side-Angle axiom of congruence.

Consider two triangles as \triangle\text{ABC} and \triangle\text{ACD} as shown in Figure 1.

Now, assume that \angle\text{ABD} and \angle\text{ADB} are equal and the side AC bisects \angle\text{BAD} as shown in Figure 1.

The side AC is common to both the triangles.

The sum of three angles of a triangle is equal to 180^{\circ}.

The \angle\text{ACB} is calculated as  follows:

\angle\text{ACB}=180-(\angle\text{CAB}+\angle\text{ABC})

The \angle\text{ACD} is calculated as  follows:

\angle\text{ACD}=180-(\angle\text{CAD}+\angle\text{ADC})

The \angle\text{CAB} is equal to \angle\text{CAD} and \angle\text{ABC} is equal to \angle\text{ADC}.

Then the \angle\text{ACB} is  calculted as follows:

\begin{aligned}\angle\text{ACB}&=180-(\angle\text{CAB}+\angle\text{ABC})\\&=180-(\angle\text{CAD}+\angle\text{ADC})\\&=\angle\text{ACD}\end{aligned}

Therefore, all the three angles of the \triangle\text{ABC} are equal to corresponding angles of \triangle\text{ADB}.

If all the angles of triangle are equal to corresponding angles of another triangle, then it is not necessary that the triangles are congruent.  

So for triangles to be congruent from three equal parts there should be one side.

Thus, AAS congruence theorem can be used to prove that the triangles are congruent.

Therefore, the correct option is \boxed{\bf option B} i.e., AAS.

Learn more:

1. Problem about triangles brainly.com/question/7437053

2. The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 3. Which expression is equivalent to this product after it has been fully simplified? brainly.com/question/1394854

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Triangles

Keywords: Triangles, congruence, two angles, one side, AAS, theorem, ASA, SSS, SAS, HL, prove, non-included side.

kodGreya [7K]3 years ago
3 0

Answer:-B )" AAS congruence theorem" an be used to prove that the triangles are congruent .

AAS congruence theorem tells that if two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle then the triangles are congruent.

Therefore option B is the correct answer. "AAS congruence" theorem an be used to prove that the triangles are congruent .


You might be interested in
Solve for x.​
AfilCa [17]
You need to put the numbers it give you, algo will am I supposed to solve that
3 0
3 years ago
Can someone PLEASE help me with THIS QUESTION
s2008m [1.1K]

Answer:

3.5

Step-by-step explanation:

you will go like sum of frequency multiplied by score divided by sum of frequency

4 0
2 years ago
Curtis has $600 and is spending $30 per
vivado [14]
After five weeks they will have the same amount of money.
3 0
3 years ago
If 7 liters of petrol cost $14.70, calculate the cost of 15 liters of petrol.​
Alex73 [517]

Hi

7 = 14.70

15= X

so :  X =  15*14.70 /7 = 31.5

15 liters  of petrol cost  31.5

5 0
3 years ago
Read 2 more answers
Melinda spend $14.25 on school supplies Dr spend $2.30 more than Melinda
zloy xaker [14]
14.25+2.30=16.55     so, dr spent $16.55 on school supplies
3 0
3 years ago
Read 2 more answers
Other questions:
  • HELP PLEASE AND THANK YOU!!!!!!
    5·1 answer
  • I really need help on this question
    9·1 answer
  • Which equation is parallel to y−4 = 2(x+1) and goes through the point (-2, -14)?
    15·1 answer
  • Janessa bought for 4 stamps for $1.48 at this rate how much would 10 stamps cost
    5·1 answer
  • The formula for the volume of a pyramid is V = 1/3 Bh, where B is the area of the base of the pyramid and h is the height of the
    5·1 answer
  • What is the GCF of xy3 and x3y?
    6·2 answers
  • If x= 2 what does y equal
    14·1 answer
  • What is the midpoint of 2,-6 and -8,5
    7·2 answers
  • Need the answer for numbers 4,8,and 12
    6·1 answer
  • Los Angeles, California, has an average daily temperature between 70 degrees F and 80 degrees F throughout most of the year. The
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!