Define isosceles triangle

Paul Mazzola • • • • • Isosceles triangle Isosceles triangles have equal legs (that's what the word "isosceles" means). Yippee for them, but what do we know about their base angles? How do we know those are equal, too? We reach into our geometer's toolbox and take out the Isosceles Triangle Theorem. No need to plug it in or recharge its batteries -- it's right there, in your head! Here we have on display the majestic isosceles triangle, △DUK. You can draw one yourself, using △DUK as a model. Isosceles Triangle With Properties Hash marks show sides ∠DU ≅ ∠DK, which is your tip-off that you have an isosceles triangle. If these two sides, called legs, are equal, then this is an isosceles triangle. What else have you got? Properties of an isosceles triangle Let's use △DUK to explore the parts: • Like any triangle, △DUK has three interior angles: ∠D, ∠U, and ∠K • All three interior angles are acute. • Like any triangle, △DUK has three sides: DU, UK, and DK • ∠DU ≅ ∠DK, so we refer to those twins as legs. • The third side is called the base (even when the triangle is not sitting on that side). • The two angles formed between base and legs, ∠DUK and ∠DKU, or ∠D and ∠K for short, are called base angles. Isosceles triangle theorem Knowing the triangle's parts, here is the challenge: how do we prove that the base angles are congruent? That is the heart of the Isosceles Triangle Theorem, which is built as a conditional (if, then) statement: The Isosceles Triangle Theorem states: If t...

In this explainer, we will learn how to use the isosceles triangle theorems to find missing lengths and angles in isosceles triangles. We know that there are four different types of triangles: equilateral, isosceles, scalene, and right triangles. The properties of the angles and sides determine what type a particular triangle is. In this definition, we have been given some useful terminology for the sides of an isosceles triangle. Knowing which of the sides in an isosceles triangle is equal to another (a leg), or whether it is the third side (the base), gives us a way to reference these sides, and, as we will see later, to consider important properties about the angles. We typically think of isosceles triangles drawn with the base as the horizontal side, but, of course, the orientation of the triangle does not matter. Congruent sides in the isosceles triangle would always be referred to as the legs, regardless of the position they take. Identify the legs of the triangle. • 𝐴 𝐵 and 𝐵 𝐶 • 𝐴 𝐵 and 𝐴 𝐶 • 𝐵 𝐶 and 𝐴 𝐶 Answer In this triangle, we can observe that there are two sides of equal length: the lengths of 𝐴 𝐵 and 𝐵 𝐶 are both given as 2 cm. By definition, a triangle that has two congruent sides is an isosceles triangle. These two congruent sides are called the legs of the triangle. Therefore, we can give the answer that the legs of the triangle are 𝐴 𝐵 and 𝐵 𝐶. That aside, we can note that the third side of an isosceles triangle is referred to as the base. In the figure ...

Recent Examples on the Web Geographically, Richland, Hammonton, and Absecon don't form an isosceles triangle. — Phil Anastasia, Philly.com, 26 May 2017 These examples are programmatically compiled from various online sources to illustrate current usage of the word 'isosceles.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Etymology borrowed from Late Latin isoscelēs, borrowed from Greek isoskelḗs"having equal legs, (of a triangle) having two equal sides, (of numbers) divisible into equal parts, even," from iso- -skelēs, adjective derivative of skélos (neuter s-stem) "leg," going back to an Indo-European base *skel-"bent," whence also Armenian šeł"slanting, crooked"; with o-grade, Greek skoliós"bent, crooked, askew, devious"; perhaps with a velar extension Germanic *skelga-/*skelha-, whence Old English sceolh"oblique, wry," Old Frisian skilich"squinting," Old High German skelah"crooked, oblique," Old Icelandic skjalgr"wry, oblique" Note: The Indo-European etymon is also conventionally compared with Latin scelus"misfortune resulting from the ill will of the gods, curse, wicked or accursed act, crime, villainy," a neuter s-stem that appears to match exactly Greek skélos, though if "crime" is secondarily developed from a sense "misfortune," with religious connotations, a connection with crookedness is less likely.

I'm a bit confused: the bisector line segment is perpendicular to the bottom line of the triangle, the bisector line segment is equal in length to itself, and the angle that's being bisected is divided into two angles with equal measures. Based on this information, wouldn't the Angle-Side-Angle postulate tell us that any two triangles formed from an angle bisector are congruent? And yet, I know this isn't true in every case. A little help, please? BD is not necessarily perpendicular to AC. Quoting from Age of Caffiene: "Watch out! The bisector is not [necessarily] perpendicular to the bottom line... Imagine you had an isosceles triangle and you took the angle bisector, and you'll see that the two lines are perpendicular. However, if you tilt the base, the bisector won't change so they will not be perpendicular anymore : ) " Unfortunately the mistake lies in the very first step.... Sal constructs CF parallel to AB not equal to AB. We know that BD is the angle bisector of angle ABC which means angle ABD = angle CBD. Now, CF is parallel to AB and the transversal is BF. So we get angle ABF = angle BFC ( alternate interior angles are equal). But we already know angle ABD i.e. same as angle ABF = angle CBD which means angle BFC = angle CBD. Therefore triangle BCF is isosceles while triangle ABC is not. Hope this helps you and clears your confusion! Best wishes!! :) i think you assumed AB is equal length to FC because it they're parallel, but that's not true. imagine extending A ...