Question

for each triangle, check all that apply.
triangle a: sides 6, 6, 10; options: scalene, isosceles, equilateral
triangle b: sides 7, 5, 11; options: scalene, isosceles, equilateral
triangle c: angles 60°, 60°, 60°; options: scalene, isosceles, equilateral
triangle d: angles 60°, 30°, 90° (right angle); options: scalene, isosceles, equilateral

Explanation:

To solve this, we analyze each triangle based on side lengths (for scalene/isosceles/equilateral) and angles:

Triangle A

• Sides: \( 6, 6, 10 \). Two sides are equal.
• Classification: Isosceles (since two sides are equal; scalene has all sides different, equilateral has all sides equal).

Triangle B

• Sides: \( 7, 5, 11 \). All sides are different.
• Classification: Scalene (all sides unequal; isosceles needs at least two equal, equilateral needs all three equal).

Triangle C

• Angles: \( 60^\circ, 60^\circ, 60^\circ \) (sum to \( 180^\circ \)). In a triangle, equal angles imply equal sides.
• Classification: Isosceles (at least two equal sides) and Equilateral (all three sides equal, since all angles are \( 60^\circ \)).

Triangle D

• Angles: \( 90^\circ, 60^\circ, 30^\circ \). All angles are different, so all sides are different (by the Law of Sines).
• Classification: Scalene (all sides unequal; isosceles needs two equal sides, equilateral needs all three equal).

Final Selections:

• Triangle A: \(\boldsymbol{\text{Isosceles}}\) (uncheck Scalene, check Isosceles, uncheck Equilateral).
• Triangle B: \(\boldsymbol{\text{Scalene}}\) (check Scalene, uncheck Isosceles, uncheck Equilateral).
• Triangle C: \(\boldsymbol{\text{Isosceles}}\) and \(\boldsymbol{\text{Equilateral}}\) (uncheck Scalene, check Isosceles, check Equilateral).
• Triangle D: \(\boldsymbol{\text{Scalene}}\) (check Scalene, uncheck Isosceles, uncheck Equilateral).

(Visually, mark the checkboxes as follows:

• Triangle A: Isosceles ✔️
• Triangle B: Scalene ✔️
• Triangle C: Isosceles ✔️, Equilateral ✔️
• Triangle D: Scalene ✔️)

Answer:

To solve this, we analyze each triangle based on side lengths (for scalene/isosceles/equilateral) and angles:

Triangle A

• Sides: \( 6, 6, 10 \). Two sides are equal.
• Classification: Isosceles (since two sides are equal; scalene has all sides different, equilateral has all sides equal).

Triangle B

• Sides: \( 7, 5, 11 \). All sides are different.
• Classification: Scalene (all sides unequal; isosceles needs at least two equal, equilateral needs all three equal).

Triangle C

• Angles: \( 60^\circ, 60^\circ, 60^\circ \) (sum to \( 180^\circ \)). In a triangle, equal angles imply equal sides.
• Classification: Isosceles (at least two equal sides) and Equilateral (all three sides equal, since all angles are \( 60^\circ \)).

Triangle D

• Angles: \( 90^\circ, 60^\circ, 30^\circ \). All angles are different, so all sides are different (by the Law of Sines).
• Classification: Scalene (all sides unequal; isosceles needs two equal sides, equilateral needs all three equal).

Final Selections:

• Triangle A: \(\boldsymbol{\text{Isosceles}}\) (uncheck Scalene, check Isosceles, uncheck Equilateral).
• Triangle B: \(\boldsymbol{\text{Scalene}}\) (check Scalene, uncheck Isosceles, uncheck Equilateral).
• Triangle C: \(\boldsymbol{\text{Isosceles}}\) and \(\boldsymbol{\text{Equilateral}}\) (uncheck Scalene, check Isosceles, check Equilateral).
• Triangle D: \(\boldsymbol{\text{Scalene}}\) (check Scalene, uncheck Isosceles, uncheck Equilateral).

(Visually, mark the checkboxes as follows:

• Triangle A: Isosceles ✔️
• Triangle B: Scalene ✔️
• Triangle C: Isosceles ✔️, Equilateral ✔️
• Triangle D: Scalene ✔️)