Prove the angles equal to prove the sides triangle problem

In summary, the conversation discusses a mensuration problem involving a triangle ABC with angle B=90 degrees, AB=20 cm, and BD=14.5 cm. The book states that BD=AD=DC and AC=2BD=29, leading to a discussion about how this was determined and how to use this information to solve the problem. The conversation also includes a suggestion to make a rectangle ABCE and use the properties of diagonals to solve the problem.
  • #1
1/2"
99
0
This is an mensurational problem of triangles.

Homework Statement


In triangle ABC, anngle B=90degrees and D is the mid point of AC .If AB=20 cm and Bd=14.5cm,find the area and perimeter of the triangle ABC.
My book says that BD=AD=DC=> AC=2BD=29 and so on
But i can't get how could they just write that BD=AD??
I am really at my wits end.
If we take this into consideration it is really easy but how do I do it when I iam not clear at the base.
I tried to prove the angles equal to prove the sides but it's not working.
Please help!
 
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  • #2


1/2" said:
This is an mensurational problem of triangles.

Homework Statement


In triangle ABC, anngleB=90degrees ,AB=(2x+1)cm.If the area and perimeter of the triangle ABC.
If the area and perimeter of the triangle ABC do what? We can't help you if you don't give us all of the information in the problem.
1/2" said:
My book says that BD=AD=DC=> AC=2BD=29 and so on
But i can't get how could they just write that BD=AD??
I am really at my wits end.
If we take this into consideration it is really easy but how do I do it when I iam not clear at the base.
I tried to prove the angles equal to prove the sides but it's not working.
Please help!
 
  • #3


I am really sorrrrrry!
 
  • #4


Make a rectangle ABCE by drawing a line segment AE that is parallel to BC and by another line segment CE that is parallel to AB. In my drawing the right angle is on the left, angle A is on the right, and angle C is above the right angle.

Extend the line segment BD to make BE. The segments AC and BE are the diagonals of a rectangle, and they both cross at D. What can you say about the lengths of BD and DE? You already know that AD and DC are equal.

Is that enough to get you going?
 
  • #5


So you mean BD=BE
But what next...
(i am really sorry but i am real slow learner)
 
  • #6


Is there something wrong i have done??:cry:
Please be free to tell
 
  • #7


1/2" said:
So you mean BD=BE
But what next...
(i am really sorry but i am real slow learner)
No, BD != BE. You should have a rectangle ABCE. BE is the length of a diagonal of the rectangle, and AC is the other diagonal. What do you know about the diagonals of a rectangle?
 
  • #8


Ok! So now I understand!
Thank you very much Mark44!:smile::smile:
 
  • #9


You're welcome!
 

Related to Prove the angles equal to prove the sides triangle problem

1. How do you prove the angles of a triangle equal to prove the sides?

To prove the angles of a triangle equal to prove the sides, you must use the angle-side-angle (ASA) or side-angle-side (SAS) theorem. This involves showing that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

2. What is the importance of proving the angles equal to prove the sides in a triangle?

Proving the angles equal to prove the sides in a triangle is important because it is a fundamental concept in geometry. It allows us to understand the relationship between the angles and sides of a triangle, which is essential in solving various geometric problems.

3. Can you use any other theorems to prove the angles equal to prove the sides of a triangle?

Yes, you can also use the angle-angle-side (AAS) theorem or the side-side-angle (SSA) theorem to prove the angles equal to prove the sides of a triangle. However, these theorems have more restrictions and may not be applicable in all cases.

4. Is it necessary to prove the angles equal to prove the sides in all triangles?

No, it is not necessary to prove the angles equal to prove the sides in all triangles. This proof is only applicable in triangles where the given information satisfies the conditions of the ASA, SAS, AAS, or SSA theorem.

5. How does proving the angles equal to prove the sides help in solving real-life problems?

Proving the angles equal to prove the sides is essential in solving real-life problems that involve triangles, such as calculating the height of buildings, determining distances, and designing structures. It allows us to accurately measure and analyze the relationships between the angles and sides of a triangle.

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