The two legs must be corresponding sides.
If the triangle is the same size, and it's sides are congruent to the other, then yes they are congruent to each other.
For segments or angles, "congruent" means that they have the same measure.For more complicated figures, such as triangles, "congruent" means that all corresponding sides and angles are congruent. "Corresponding" means that you make an assignment, from angles and sides of one triangle, to angles and sides of the other triangle. For example, you might label the sides of one triangle a1, b1, c1, and the sides of other triangle a2, b2, c2 - and you consider the "a" sides to be "corresponding".
Yes. The triangles have the same angle measures but different, similar side lengths. Think of two different sized equilateral triangles. One can have side lengths of 6 inches while the other has side lengths of 20 inches, but they still have congruent angles of 60 degrees. Each ratio of side lengths is equal [6/20=6/20=6/20].
Yes, you have two congruent angles in each triangle, one right and one acute so the third angles must be equal also.
False. Assume that you had a two right triangles with one congruent acute (<90 degrees) angle in common. Let x represent the number of degrees in this angle in both triangles (which we can do since the angles are congruent). Let y represent the degree of the other angle in the first triangle and let z represent the degree of the other angle in the second triangle. We know that the sum of the degrees of the angles in a triangle is 180. So for the first triangle we have, 90+x+y = 180 For the second triangle, 90+x+z=180 Therefore, 90+x+y=90+x+z Subtract the 90+x from each side: y=z Therefore the degrees of the angles of the two triangles both are 90 [because they are both right triangles], x [because we said that this is the number of degrees of the congruent angles given in the problem], and y [because y=z]. Because the three angles of both triangles have the same measurement, the triangles must be similar.
The SAS theorem is used to prove that two triangles are congruent. If the triangles have a side-angle-side that are congruent (it must be in that order), then the two triangles can be proved congruent. Using this theorem can in the future help prove corresponding parts are congruent among other things.
1. There are two right triangles. 2. They have congruent hypotenuses. 3. They have one pair of congruent legs.
It is a congruence theorem for triangles. It states that if you have two triangles in which two sides of one are congruent to two sides of the other, and the angles included by the sides are equal, then the triangles are congruent.
The hypotenuse angle theorem, also known as the HA theorem, states that 'if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.'
If two right triangles have (hypotenuse and a leg of one) = (hypotenuse and the corresponding leg of the other) then the triangles are congruent.
sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.
Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.
Excuse me, but two triangles that have A-A-S of one equal respectively to A-A-S of the other are not necessarily congruent. I would love to see that proof!
A square and rectangle both have congruent triangles in them.
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
A trapezoid can be divided into 2 triangles but they are not normally congruent to each other.
no because isosceles triangles only have two congruent sides and the other one is different