Congruency in Isosceles and Equilateral Triangles

Explore the properties of isosceles and equilateral triangles, including angle and side congruency, through various problems.

Grade 10 Math GeometryCongruency in Isosceles and Equilateral Triangles

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Includes

True / FalseMultiple ChoiceFill in the BlanksShort AnswerLong Answer

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10CCSS.MATH.CONTENT.HSG.SRT.B.5

Topics

GeometryTrianglesCongruencyIsoscelesEquilateral

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Congruency in Isosceles and Equilateral Triangles

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. All equilateral triangles are isosceles triangles.

True

False

2. An isosceles triangle always has three congruent angles.

True

False

3. In an isosceles triangle, if one base angle measures 50 degrees, what is the measure of the vertex angle?

50 degrees

80 degrees

60 degrees

100 degrees

4. If an equilateral triangle has a perimeter of 24 cm, what is the length of each side?

6 cm

8 cm

12 cm

24 cm

5. In an isosceles triangle, the angles opposite the congruent sides are .

6. An equilateral triangle has congruent sides and congruent angles.

7. Consider an isosceles triangle ABC where AB = AC. If the measure of angle B is 70 degrees, what are the measures of angles A and C? Justify your answer.

8. An equilateral triangle DEF has sides of length (2x + 5) units. If the perimeter of the triangle is 33 units, find the value of x and the length of each side.

9. Prove that if a triangle is equilateral, then it is also equiangular.