Question

identify any lines of symmetry this figure has. 5 from unit 1, lesson 15 a triangle has a line of symmetry. select all conclusions that must be true. a all sides of the triangle have the same length. b all angles of the triangle have the same measure. c no sides of the triangle have the same length. d no angles of the triangle have the same measure. e two sides of the triangle have the same length. f two angles of the triangle have the same measure

Explanation:

Step1: Recall line - symmetry in triangles

A triangle with a line of symmetry is an isosceles triangle. An equilateral triangle (a special - case of isosceles) also has lines of symmetry.

Step2: Analyze side - length properties

In an isosceles triangle, two sides have the same length. An equilateral triangle has all sides equal, but we only know there is at least one line of symmetry, so we can't assume all sides are equal. So, two sides of the triangle have the same length (E is correct), and we can't say all sides are equal (A is incorrect) or no sides are equal (C is incorrect).

Step3: Analyze angle - measure properties

In an isosceles triangle, the base angles (the angles opposite the equal sides) are equal. So, two angles of the triangle have the same measure (F is correct), and we can't say all angles are equal (B is incorrect) or no angles are equal (D is incorrect).

Answer:

E. Two sides of the triangle have the same length, F. Two angles of the triangle have the same measure