📐 Topic Summary
An isosceles triangle is a triangle that has two sides of equal length. The Isosceles Triangle Theorem states that if two sides of a triangle are congruent (equal in length), then the angles opposite those sides are congruent (equal in measure). Conversely, if two angles of a triangle are congruent, then the sides opposite those angles are congruent. This theorem is fundamental in geometry for solving problems related to triangles and their properties.
This worksheet is designed to test your knowledge of the Isosceles Triangle Theorem. Good luck!
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Isosceles Triangle |
a. An angle greater than 90 degrees and less than 180 degrees. |
| 2. Congruent |
b. A line segment from a vertex to the midpoint of the opposite side. |
| 3. Obtuse Angle |
c. Having the same measure or size. |
| 4. Median |
d. A triangle with at least two sides of equal length. |
| 5. Vertex Angle |
e. The angle formed by the two congruent sides in an isosceles triangle. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
In an isosceles triangle, the two equal sides are called ______. The angles opposite these sides are called ______ angles, and according to the Isosceles Triangle Theorem, these angles are ______. The angle formed by the two congruent sides is called the ______ angle. If the base angles are known, you can find the vertex angle by using the fact that the sum of all angles in a triangle is ______ degrees.
🤔 Part C: Critical Thinking
Explain how the Isosceles Triangle Theorem can be used in real-world applications, such as architecture or engineering. Provide a specific example.