Table of Contents
- 1 Which theorem states if two angles of a triangle are congruent then the sides opposite those angles are congruent?
- 2 What happens when 2 sides of a triangle are congruent?
- 3 What is the HL theorem?
- 4 When two sides of a triangle are congruent what can you conclude about the angles opposite those sides?
- 5 What is a hypotenuse leg?
Which theorem states if two angles of a triangle are congruent then the sides opposite those angles are congruent?
Isosceles Triangle Theorem
Isosceles Triangle Theorem. If two sides of a triangle are congruent , then the angles opposite to these sides are congruent. Proof: Let S be the midpoint of ¯PQ .
Are angles opposite of congruent sides congruent?
If two sides of a triangle are congruent, the angles opposite these sides are congruent. If two angles of a triangle are congruent, the sides opposite these angles are congruent. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
What happens when 2 sides of a triangle are congruent?
If two sides of the triangle are congruent, then the triangle is isosceles, so the angles at the third side (base) are congruent. If the triangle is not only isosceles but equilateral the third angle is also congruent.
What is the reason if two sides of a triangle are congruent then the angles opposite those sides are also congruent?
Therefore, △ABDand △ACD are congruent by SSS (side side side) property. Hence, ∠ABD=∠ACD. Therefore, the angles are congruent. So, we can say that if two sides of the triangle are congruent, then the triangle is isosceles, and the angles at the third side (base) are congruent.
What is the HL theorem?
What is the HL Postulate? The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
What do you call a theorem that states if two angles of a triangle are congruent to two angles of another triangle then the triangles are similar?
Vocabulary Language: English ▼ English
| Term | Definition |
|---|---|
| SAS Similarity Theorem | The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar. |
When two sides of a triangle are congruent what can you conclude about the angles opposite those sides?
If two sides of a triangle are congruent, then the angles opposite those sides are congruent. The converse of the base angles theorem, states that if two angles of a triangle are congruent, then sides opposite those angles are congruent.
What do you call if two triangles are congruent then the corresponding parts are congruent?
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
What is a hypotenuse leg?
In a right-angled triangle, the hypotenuse is the longest side which is always opposite to the right angle. The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle’s hypotenuse and leg side.