Help Proving ABC is Acute Triangle with Altitudes

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In summary, to prove that ABC is an acute triangle with altitudes, we must show that all three angles of the triangle are less than 90 degrees and that the three altitudes intersect at a single point inside the triangle. An altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side, and it is also the height of the triangle. An acute triangle is a triangle where all three angles are less than 90 degrees, while a right triangle has one angle that measures exactly 90 degrees. Some properties of an acute triangle with altitudes include: all three angles are acute, the altitudes intersect at a single point inside the triangle, the sum of the lengths of the altitudes is equal
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Vishalrox
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I need help in this ques !

ABC is acute triangle. A1, B1, C1 are foot of altitudes. A1 is reflected about AC to get A2. Prove that B1, C1, A2 are collinear...i couldn't evn figure out how to solve it...but i need it just tell me the method no need to proove...or just tell me the idea how to proove...i need it...plez don't remove this ques...

I tried with the method of Angle chase geometry..but still couldn't get...
 
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Try using complex numbers or coordinate geometry.
 

FAQ: Help Proving ABC is Acute Triangle with Altitudes

1. How do you prove that ABC is an acute triangle with altitudes?

To prove that ABC is an acute triangle with altitudes, we must show that all three angles of the triangle are less than 90 degrees, and that the three altitudes intersect at a single point inside the triangle.

2. What is an altitude of a triangle?

An altitude of a triangle is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. It is also the height of the triangle, as it connects the vertex to the opposite side at a right angle.

3. What is the difference between an acute triangle and a right triangle?

An acute triangle is a triangle where all three angles are less than 90 degrees, while a right triangle has one angle that measures exactly 90 degrees. In an acute triangle, the sum of all three angles is less than 180 degrees, while in a right triangle, the sum is exactly 180 degrees.

4. What are some properties of an acute triangle with altitudes?

Some properties of an acute triangle with altitudes include: all three angles are acute, the altitudes intersect at a single point inside the triangle, the sum of the lengths of the altitudes is equal to the perimeter of the triangle, and the product of the lengths of the altitudes is equal to four times the area of the triangle.

5. How can I use trigonometry to prove that ABC is an acute triangle with altitudes?

You can use trigonometric ratios such as sine, cosine, and tangent to calculate the lengths of the sides and angles of ABC. If all three angles are less than 90 degrees, and the sum of the lengths of the altitudes is equal to the perimeter of the triangle, then you have proven that ABC is an acute triangle with altitudes.

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