0
How do i prove if the base angles of a triangle are congruent then the triangle is isosceles?
Wiki User
∙ 15y ago
Suppose you have triangle ABC with base BC, and angle B = angle C. Draw the altitude AD.
Considers triangles ABD and ACD
angle ABD = angle ACD (given)
angle ADB = 90 deg = angle ACD
therefore angle BAD = angle CAD
Also the side AD is common to the two triangles.
Therefore triangle ABD is congruent to triangle ACD (ASA) and so AB = AC.
That is, triangle ABC is isosceles.
Wiki User
∙ 9y ago
Add your answer:
Earn +20 pts
How do you prove that the diagonals of an isosceles trapezoid are congruent?
Suppose the diagonals meet at a point X.AB is parallel to DC and BD intersects themTherefore, angle ABD ( = ABX) = BAC (= BAX)Therefore, in triangle ABX, the angles at the ends of AB are equal => the triangle is isosceles and so AX = BX.AB is parallel to DC and AC intersects themTherefore, angle ACD ( = XCD) = BDC (= XDC)Therefore, in triangle CDX, the angles at the ends of CD are equal => the triangle is isosceles and so CX = DX.Therefore AX + CX = BX + DX or, AC = BD.
What is the angle bisector concurrency theorem?
the definition of an angle bisector is a line that divides an angle into two equal halves. So you need only invoke the definition to prove something is an angle bisector if you already know that the two angles are congruent.
How do you prove that the diagonals and either base of an isosceles trapezoid form an isosceles triangle?
Consider the isosceles trapezium ABCD (going clockwise from top left) with AB parallel to CD. And let the diagonals intersect at O Since it is isosceles, AD = BC and <ADC = <BCD (the angles at the base BC). Now consider triangles ADC and BCD. AD = BC The side BC is common and the included angles are equal. So the two triangles are congruent. and therefore <ACD = <BDC Then, in triangle ODC, <OCD (=<ACD = <BDC) = <ODC ie ODC is an isosceles triangle. The triangle formed at the other base can be proven similarly, or by the fact that, because AB CD and the diagonals act as transversals, you have equal alternate angles.
Which theorem is used to prove the AAS triangle congruence postulate theorem?
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
Which theorem is used to prove that aas triangle congruence postulate theorem?
AAS: If Two angles and a side opposite to one of these sides is congruent to thecorresponding angles and corresponding side, then the triangles are congruent.How Do I know? Taking Geometry right now. :)
How do you prove an isosceles triangle?
an isisceles triangle is a triangle with atleast two sides congruent.
How do you prove the diagonals of an isosceles triangle congruent?
You can't because triangles do not have diagonals but an isosceles triangle has 2 equal sides
If two angle bisectors of a triangle are congruent then prove that triangle is isosceles?
If two angle bisectors of a triangle are congruent, then the triangle is isosceles. This is because the angle bisectors of a triangle are concurrent and the angle bisectors of a triangle that are congruent divide the opposite sides of the triangle into two equal segments. So if two angle bisectors are congruent, the sides opposite those angles are also equal, making the triangle isosceles.
How can proving two triangles congruent can help prove parts of the triangle congruent?
When you prove a triangle is congruent to another, it can help you prove parts of the triangle congruent by checking the ratio between all sides and angles. Thank you for asking
Is an equilateral triangle always or sometimes called an isosceles?
If you can only prove two sides of an apparently equilateral triangle to be congruent then you have to use isosceles.
How do you prove a trapezoid is isoceles?
To prove a trapezoid is isosceles, you need to show that the legs (the non-parallel sides) are congruent. This can be done by demonstrating that the base angles opposite these sides are congruent. You can use the triangle congruence postulates or the properties of parallel lines and transversals to establish the equality of these angles.
How can you prove that a triangle is an isosceles triangle with some examples?
An isosceles triangle has 3 sides 2 of which are equal in length An isosceles triangle has 3 interior angles 2 of which are the same size
How can you prove a triangle ABC is isosceles if angle BAD is congruent to angle CAD and line AD is perpendicular to line Bc?
Given: AD perpendicular to BC; angle BAD congruent to CAD Prove: ABC is isosceles Plan: Principle a.s.a Proof: 1. angle BAD congruent to angle CAD (given) 2. Since AD is perpendicular to BC, then the angle BDA is congruent to the angle CDA (all right angles are congruent). 3. AD is congruent to AD (reflexive property) 4. triangle BAD congruent to triangle CAD (principle a.s.a) 5. AB is congruent to AC (corresponding parts of congruent triangles are congruent) 6. triangle ABC is isosceles (it has two congruent sides)
How can you prove that a triangle is an isosceles triangle?
It has 3 sides 2 of which are equal in length It has 3 angles 2 of which are the same size
Angle bisector of angleA of triangleABC is perpendicular to BC prove it is isosceles?
Let D represent the point on BC where the bisector of A intersects BC. Because AD bisects angle A, angle BAD is congruent to CAD. Because AD is perpendicular to BC, angle ADB is congruent to ADC (both are right angles). The line segment is congruent to itself. By angle-side-angle (ASA), we know that triangle ADB is congruent to triangle ADC. Therefore line segment AB is congruent to AC, so triangle ABC is isosceles.
What is the definition of AAS Congruence postulate of trianges?
It is a theorem, not a postulate, since it is possible to prove it. If two angles and a side of one triangle are congruent to the corresponding angles and side of another triangle then the two triangles are congruent.
How do you Prove triangle ACD is congruent to triangle BDC?
Because Corresponding Parts of Congruent Triangles, there are five ways to prove that two triangles are congruent. Show that all sides are congruent. (SSS) Show that two sides and their common angle are congruent. (SAS) Show that two angles and their common side are congruent. (ASA) Show that two angles and one of the non common sides are congruent. (AAS) Show that the hypotenuse and one leg of a right triangle are congruent. (HL)
