QuestionIdentify the properties of isosceles triangles: all sides congruent, none congruent, two sides congruent, angles , none congruent, two angles congruent.
Studdy Solution
STEP 1
Assumptions1. An isosceles triangle is a triangle that has two sides of equal length.
. The angles opposite to the equal sides in an isosceles triangle are equal.
3. The third side of an isosceles triangle can be of any length, not necessarily equal to the other two sides.
4. The third angle of an isosceles triangle can be of any measure, not necessarily equal to the other two angles.
STEP 2
Let's examine each of the properties one by one.
The first property states that all sides of an isosceles triangle are congruent. This is not true for an isosceles triangle as only two sides are of equal length, not all three.
STEP 3
The second property states that none of the sides of an isosceles triangle are congruent. This is also not true for an isosceles triangle as two sides are of equal length.
STEP 4
The third property states that two sides of an isosceles triangle are congruent. This is true for an isosceles triangle as it is defined as a triangle with two sides of equal length.
STEP 5
The fourth property states that all angles of an isosceles triangle are . This is not necessarily true for an isosceles triangle. While it is possible for an isosceles triangle to have all angles measuring , it would then be a special case of an isosceles triangle known as an equilateral triangle.
STEP 6
The fifth property states that none of the angles of an isosceles triangle are congruent. This is not true for an isosceles triangle as the angles opposite to the equal sides are equal.
STEP 7
The sixth property states that two angles of an isosceles triangle are congruent. This is true for an isosceles triangle as the angles opposite to the equal sides are equal.
So, the properties that apply to isosceles triangles are1. Two sides are congruent.
2. Two angles are congruent.
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