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In this section, students explore the properties of isosceles triangles, learning that the angles opposite equal sides are equal. The converse is also discussed, highlighting that if two angles in a triangle are equal, their opposite sides are equal, leading to important conclusions related to triangle congruence.
In this section, we focus on the properties of isosceles triangles, which are triangles with at least two equal sides. 1. Isosceles Triangle Definition: A triangle with two equal sides (e.g., in triangle ABC, sides AB = AC).
Through these discussions, students gain a deeper understanding of triangle properties and congruence criteria, preparing them for more complex geometric concepts.
Isosceles Triangle: A triangle with two equal sides, having equal opposite angles.
Angle Properties: Opposite angles in an isosceles triangle are equal, showing that 'angles equal, sides equal'.
Theorems 7.2 and 7.3: The relationships between sides and angles in isosceles triangles are defined and proven.
If the sides are the same, the angles too will claim!
Once upon a time, in a land of angles and sides, there lived a triangle named Isosceles, who always kept its two angles equal to please!
Remember 'LEA' for Legs Equal, Angles Equal when studying isosceles triangles.
Example: In triangle ABC, if AB = AC and angle B = angle C, then the triangle is isosceles.
Example: Construct triangle ABC where B and C are both 50°, concluding that AB = AC.
Term: Isosceles Triangle
Definition: A triangle with at least two sides of equal length.
A triangle with at least two sides of equal length.
Term: Vertex Angle
Definition: The angle between the equal sides of an isosceles triangle.
The angle between the equal sides of an isosceles triangle.
Term: SAS Congruence Criterion
Definition: A criterion for triangle congruence stating that if two sides and the included angle are equal in two triangles, then the triangles are congruent.
A criterion for triangle congruence stating that if two sides and the included angle are equal in two triangles, then the triangles are congruent.
Term: Theorem
Definition: A statement that has been proven on the basis of previously established statements.
A statement that has been proven on the basis of previously established statements.