What is hl in geometry

Next Unit Polygons. Brian McCall. Thank you for watching the video. Start Your Free Trial Learn more. Brian McCall Univ. Explanation Transcript In right triangles , if two legs are congruent and if the two hypotenuses are congruent, then the triangles are congruent. Geometry Triangles. Science Biology Chemistry Physics. And just as we have two equal legs, an isosceles triangle has two equal legs sides , as Math is Fun nicely points out.

Well, if a triangle has exactly two congruent sides, then the base angles are congruent. The base angles are the two angles formed between the legs of the triangle and the non-congruent side. And more importantly, these base angles are congruent. The Isosceles Triangle Theorem, sometimes called the Base Angle Theorem, states that if two sides of a triangle are congruent, then the angles opposite them are also congruent.

Moreover, the Equilateral Triangle Theorem states if a triangle is equilateral i. Hold on, you say, that so-called theorem only spoke about two legs, and didn't even mention an angle. Aha, have you forgotten about our given right angle?

Every right triangle has one, and if we can somehow manage to squeeze that right angle between the hypotenuse and another leg Of course you can't, because the hypotenuse of a right triangle is always always! So we have to be very mathematically clever. We have to enlist the aid of a different type of triangle. We must first prove the HL Theorem. Once proven, it can be used as much as you need. To prove that two right triangles are congruent if their corresponding hypotenuses and one leg are congruent, we start with … an isosceles triangle.

We are about to turn those legs into hypotenuses of two right triangles. Can you guess how? Construct an altitude from side A K. Recall that the altitude of a triangle is a line perpendicular to the base, passing through the opposite angle. That altitude, J C , complies with the Isosceles Triangle Theorem, which makes the perpendicular bisector of the base the angle bisector of the vertex angle.

So, all three interior angles of each right triangle are congruent, and all sides are congruent. How about that , J A C K? We originally used the isosceles triangle to find the hypotenuse and a single leg congruent, and from that, we built proof that both triangles are congruent.

You also notice, masterful detective that you are, the sides opposite the right angles are congruent:.