Math by First Principles
Level 1 · Foundational ← Back to lesson

Isosceles and Equilateral Triangles: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    In triangle ABC, the equal sides are

    AB=AC.\begin{aligned} AB&=AC. \end{aligned}

    Which side is the base associated with these equal sides?

    Find the base from the equal sidesTriangle ABC has matching ticks on AB and AC. No base or angle conclusion is marked.ABCNot to scale
  2. 2

    Triangle MNP has the equal sides

    MN=NP.\begin{aligned} MN&=NP. \end{aligned}

    Which angles are the congruent base angles?

    Match the opposite anglesTriangle MNP has matching ticks on MN and NP, meeting at N. No angle equality is marked.NMPNot to scale
  3. 3

    An isosceles triangle has a vertex angle of 84 degrees. What is each base angle?

    Use the vertex angleAn isosceles triangle has two matching side ticks and its vertex angle labeled 84 degrees. No base-angle measures are shown.ABC84°Not to scale
  4. 4

    An isosceles triangle has a base angle of 39 degrees. What is its vertex angle?

    Use the given base angleAn isosceles triangle has two matching side ticks and one base angle labeled 39 degrees. No other angle measures are shown.ABC39°Not to scale
  5. 5

    What is the measure of each interior angle in an equilateral triangle?

    Start with equal sidesAn equilateral triangle has a matching tick on each side. No angle measure is marked.ABCNot to scale
  6. 6

    A triangle has three congruent interior angles. Which side classification must apply?

    Start with equal anglesA triangle has a matching angle arc at each vertex. No equal-side ticks are drawn.ABCNot to scale
  7. 7

    Which statement matches the inclusive definition used in this course?

  8. 8

    What defines a median of a triangle?

  9. 9

    What defines an altitude from a triangle vertex?

  10. 10

    Triangle DEF has the equal sides

    DE=DF.\begin{aligned} DE&=DF. \end{aligned}

    DG is the internal bisector of angle EDF, with G on EF. Which conclusion follows?

    Track the given vertex bisectorTriangle DEF has matching ticks on DE and DF. DG meets EF at G and bisects angle EDF, marked by matching vertex arcs. No base-half or right-angle marks are drawn.DEFGNot to scale
  11. 11

    When proving the base-angle theorem by drawing the vertex angle bisector, which criterion proves the two smaller triangles congruent?

    Compare the split triangleAn isosceles triangle has equal-side ticks and its vertex angle divided into equally marked parts by a segment to the base. No base-angle or right-angle conclusion is marked.ABCDNot to scale
  12. 12

    In triangle XYZ, angles Y and Z are congruent. Which equality follows?

    Use the equal angle givensTriangle XYZ has matching arcs at Y and Z. No equal-side ticks are drawn.XYZNot to scale
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