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
navik [9.2K]
3 years ago
9

Which pair of triangles are congruent by ASA ?

Mathematics
2 answers:
Alika [10]3 years ago
5 0

The pair of triangles that are congruent by ASA is \boxed{\bf option (d)}.

Further explanation:

Triangles are congruent when all the corresponding sides and interior angles are equal.

There are four theorems by which we say that the triangles are congruent.

1. Side-Side-Side(SSS)

If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.

2. Angle-Side-Angle(ASA)

If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.

3. Side-Angle-Side(SAS)

If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.

4. Hypotenuse Leg (HL)

If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.

Option (a)

The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.

Both the figures don’t have a single property from the above mentioned properties.

Therefore, option (a) is incorrect.

Option (b)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA.

Thus, option (b) is incorrect.

Option (c)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA rule.

Thus, option (c) is incorrect.

Option (d)

The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by ASA rule.

Thus, option (d) is correct.

Hence, the \boxed{\bf option (d)} is correct as the triangles are congruent by ASA rule.

Learn more:

1. A problem to determine the equation of line brainly.com/question/1646698

2. A problem on ray brainly.com/question/1251787

3. A problem to determine intercepts of a line brainly.com/question/1332667  

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Angles and Triangles

Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.

NNADVOKAT [17]3 years ago
4 0

Answer:

A,D

Step-by-step explanation:

ASA or "angle-side-angle" tells us that two triangles are congruent if two angles and the side contained between them are equal. Hence, we are looking for two angles that coincide in echa triangle, this is the case for the triangles in a. and b., and that the side that lies between the two angles is also equal in both triangles, again this is the case for a. and b.

You might be interested in
Look at this square. Find the value of a.
yaroslaw [1]
Perimeter is the total length of all sides. 72 divided by 4 equal sides of a square will give you the value of a. 72 divided by 4 is 18. The value of a is 18 yards.
8 0
2 years ago
Read 2 more answers
Which of the following vectors are orthogonal to (-1,3)? Check all that apply.
Aliun [14]
First vector orthogonal<span> to ⟨−</span>3<span>,4</span>
7 0
3 years ago
What does AE equal to ?
sasho [114]

Answer:

i think its 70

Step-by-step explanation:

35+35=70

because line ## is same as ## and ##

3 0
3 years ago
Please help with driving test!
balandron [24]

i say d                                                                                                                   ggbggggggggggggggggggggggggggggggggg                                                                                                                    

5 0
3 years ago
What properties will you use next to solve the equation
ella [17]

Answer:

To solve an equation you can use PEMDAS, standing for parenthesis, exponents, multiplication, division and addition. If it's an equation like, x/3+7+13, you could use the distributive property. By separating variables.

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Suppose the diameter of a circle is 4, What is its circumference?
    7·1 answer
  • (-11+ √-4) + (4+ √-36)
    15·1 answer
  • WILL MARK BRAINLIEST PLEASE HURRY!!!!
    9·1 answer
  • Here are the numbers of children in 14 elementary school classes.
    12·2 answers
  • Anybody know the answer to this?
    7·2 answers
  • ⁵
    14·1 answer
  • Need help asap please!
    14·2 answers
  • Determine if parallel, perpendicular, or neither.<br><br> 3y+x=12 <br> -y=8x+1
    11·1 answer
  • Find the measure of the angle
    7·1 answer
  • What is the equation of the parabola ?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!