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

SAS and ASA Congruence: Practice

12 multiple-choice questions, progressively harder.

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

    Which angle is included between sides PQPQ and PRPR?

    Locate the shared vertexTriangle PQR has P at the lower left, Q at the lower right, and R above. Sides PQ and PR are emphasized. No angle is marked.PQR
  2. 2

    Which side is included between the angles at DD and FF in triangle DEFDEF?

    The stated triangle partsTriangle DEF has D at the lower left, E at the lower right, and F above. A single arc marks angle D, and double arcs mark angle F. No side has a length label or equality tick.DEF
  3. 3

    Triangles ABCABC and DEFDEF have these given matching parts:

    AB=DEAC=DF∠A≅∠D\begin{aligned} AB&=DE \\ AC&=DF \\ \angle A&\cong\angle D \end{aligned}

    Which criterion uses exactly these givens?

    The recorded triangle partsTriangle ABC is above triangle DEF. Sides AB and DE have single ticks. Sides AC and DF have double ticks. Single arcs mark angles A and D.ABCDEF
  4. 4

    Triangles LMNLMN and XYZXYZ have these given matching parts:

    ∠L≅∠XLN=XZ∠N≅∠Z\begin{aligned} \angle L&\cong\angle X \\ LN&=XZ \\ \angle N&\cong\angle Z \end{aligned}

    Which criterion uses exactly these givens?

    The recorded triangle partsTriangle LMN is above triangle XYZ. Sides LN and XZ have single ticks. Single arcs mark angles L and X. Double arcs mark angles N and Z.LNMXZY
  5. 5

    The given side pairs and intended correspondence are:

    UV=XYVW=YZU↔XV↔YW↔Z\begin{aligned} UV&=XY \\ VW&=YZ \\ U&\leftrightarrow X \\ V&\leftrightarrow Y \\ W&\leftrightarrow Z \end{aligned}

    Which angle pair directly completes SAS?

    The recorded triangle partsTriangle UVW is above triangle XYZ. Sides UV and XY have single ticks. Sides VW and YZ have double ticks. No angles are marked.VUWYXZ
  6. 6

    Angles at A,CA,C match angles at D,FD,F, respectively. Which equality supplies the included-side pair for ASA?

    The recorded triangle partsTriangle ABC is above triangle DEF. Single arcs mark angles A and D. Double arcs mark angles C and F. No sides have equality ticks or length labels.ABCDEF
  7. 7

    A proposed SAS construction uses two positive side lengths but an included angle of 0∘0^\circ. What happens?

  8. 8

    A triangle has angles 38∘38^\circ and 87∘87^\circ at the endpoints of a known side. What is its third angle?

  9. 9

    Which information is sufficient for SAS?

  10. 10

    A congruence match sends AA to TT, BB to RR, and CC to SS. Complete the ordered statement:

    △ABC≅△ □.\triangle ABC\cong\triangle\,\square.
  11. 11

    In an SAS construction, the base is drawn and the included-angle ray starts at its left endpoint. What fixes the third vertex on that ray?

  12. 12

    When constructing a triangle from a side and its two endpoint angles, how should the two new rays open?

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