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Label the triangle ABC.
Draw the bisector of angle A to meet BC at D.
Then in triangles ABD and ACD,
angle ABD = angle ACD (equiangular triangle)
angle BAD = angle CAD (AD is angle bisector)
so angle ADB = angle ACD (third angle of triangles).
Also AD is common.
So, by ASA, triangle ABD is congruent to triangle ACD
and therefore AB = AC.
By drawing the bisector of angle B, it can be shown that AB = BC.
Therefore, AB = BC = AC ie the triangle is equilateral.
What else can I help you with?
What is the proof that equilateral triangle is also called equiangular triangle?
Equilateral means 'same length' - Therefore if the length of each side in a triangle are the same, each angle MUST also be the same.
How do you write a two column proof that has triangle AbC is equiangular for the given and EF is parallel to AC and prove triangle EFB is equiangular?
To write a two-column proof demonstrating that triangle EFB is equiangular given that triangle ABC is equiangular and line EF is parallel to AC, first list the given information in the left column. In the right column, write the corresponding statements: since EF is parallel to AC, by the Corresponding Angles Postulate, angle EFB is equal to angle ABC, and angle AEF is equal to angle CAB. Finally, since triangle ABC is equiangular, the third angle EBF will also be equal to angle ACB, proving triangle EFB is equiangular.
What are reasons used in the proof that the equilatera triangle construction constructs an equilateral triangle?
In the proof that the construction creates an equilateral triangle, key reasons include the properties of circles and congruence. When a circle is drawn with a radius equal to the length of one side of the triangle, the points where the circle intersects with the other sides ensure that all sides are equal. Additionally, by applying the congruence of triangles (such as Side-Side-Side), it can be shown that all angles are also equal, confirming the equilateral nature of the triangle. Thus, the construction relies on fundamental geometric principles to establish that the triangle is indeed equilateral.
What are the reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle?
The answer to this question is Two segments that are both congruent to a third segment must be congruent to each other All of the radii of a circle are congruent You're welcome.
What are reasons used to proof that the equilateral triangle construction actually constructs an equilateral triangle?
all the angles measure up to be the sameTwo segments that are both congruent to a third segment must be congruent to each otherAll of the radii of a circle are congruent
What is the proof that equilateral triangle is also called equiangular triangle?
Equilateral means 'same length' - Therefore if the length of each side in a triangle are the same, each angle MUST also be the same.
What are reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle triangle?
The following is the answer.
How do you write a two column proof that has triangle AbC is equiangular for the given and EF is parallel to AC and prove triangle EFB is equiangular?
To write a two-column proof demonstrating that triangle EFB is equiangular given that triangle ABC is equiangular and line EF is parallel to AC, first list the given information in the left column. In the right column, write the corresponding statements: since EF is parallel to AC, by the Corresponding Angles Postulate, angle EFB is equal to angle ABC, and angle AEF is equal to angle CAB. Finally, since triangle ABC is equiangular, the third angle EBF will also be equal to angle ACB, proving triangle EFB is equiangular.
Are reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle Check all that apply.?
An equilateral triangle is a regular polygon because it has 3 equal sides and 3 equal 60 degree angles that add up to 180 degrees.
What are reasons used in the proof that the equilatera triangle construction constructs an equilateral triangle?
In the proof that the construction creates an equilateral triangle, key reasons include the properties of circles and congruence. When a circle is drawn with a radius equal to the length of one side of the triangle, the points where the circle intersects with the other sides ensure that all sides are equal. Additionally, by applying the congruence of triangles (such as Side-Side-Side), it can be shown that all angles are also equal, confirming the equilateral nature of the triangle. Thus, the construction relies on fundamental geometric principles to establish that the triangle is indeed equilateral.
What are the reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle?
The answer to this question is Two segments that are both congruent to a third segment must be congruent to each other All of the radii of a circle are congruent You're welcome.
What are reasons used to proof that the equilateral triangle construction actually constructs an equilateral triangle?
all the angles measure up to be the sameTwo segments that are both congruent to a third segment must be congruent to each otherAll of the radii of a circle are congruent
what- fill in the blank in the following proof.?
(1) equiangular, (2) division
what- fill in the blanks in the following paragraph proof?
(1) equiangular, (2) division
What is the area of an equilateral triangle with sides of 10 inches and height of 7 inches?
I'm showing it with absolute proof. Equilateral triangle both side are same in size & same angel.It's given with the sides of 10 inches & height 7 inches. I don't need to count the height(7),just use side(10).The formula is=Area of a equilateral triangle="root over of 3" /4 * "a square"Now I use this formula,where "a" is 10. So the answers come=43.3,which is 44.So the Correct answer is=44 inches.* * * * *Mostly correct, but:43.3 should be rounded to 43, not 44.The units for the area should be square inches, not inches.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
What is the proof showing that the heights of a triangle are concurrent?
There cannot be a proof because the statement need not be true.
