An isosceles triangle is a triangle that has two sides of equal length. The angles opposite these equal sides are also equal, and this is the core idea behind the Isosceles Triangle Theorem. This theorem is super useful for solving geometric problems, especially when you need to find missing angles or prove that two sides are equal. Let's practice applying this concept!
Match the following terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Isosceles Triangle | A. The point where two sides meet in a triangle. |
| 2. Base | B. The side opposite the vertex angle in an isosceles triangle. |
| 3. Leg | C. A triangle with two congruent sides. |
| 4. Vertex Angle | D. An angle formed by the two congruent sides of an isosceles triangle. |
| 5. Base Angles | E. The two angles opposite the congruent sides in an isosceles triangle; they are congruent. |
Complete the paragraph using the words provided below:
If a triangle is _______, then the angles opposite the ________ sides are ________. In an isosceles triangle, the ________ angles are congruent. This property helps in solving various problems related to finding unknown angles and proving geometric relationships.
Word Bank: congruent, equal, base, isosceles
Imagine you have a triangular piece of land where two sides measure exactly the same. How can you use the Isosceles Triangle Theorem to ensure that you build a fence that perfectly bisects the angle formed by those two equal sides, creating two equal sections of land?
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