Question

which triangles are congruent to △a? choose all that apply. triangle b triangle c triangle d triangle e congruent figures have the same size and shape.

Explanation:

Step1: Check size and shape

Congruent figures have same size and shape. Measure side - lengths (using grid units).
For triangle \(A\), vertical side \(= 3\) units, horizontal side \(= 2\) units, hypotenuse (using Pythagoras \(a^{2}+b^{2}=c^{2}\), \(3^{2}+2^{2}=9 + 4=13\), \(c=\sqrt{13}\))

Step2: Analyze triangle \(B\)

Vertical side \(= 2\) units, horizontal side \(= 1\) unit. Sizes are different from \(A\).

Step3: Analyze triangle \(C\)

Vertical side \(= 2\) units, horizontal side \(= 3\) units. Hypotenuse: \(2^{2}+3^{2}=4 + 9 = 13\), \(c=\sqrt{13}\). Same size and shape as \(A\) (rotation / reflection possible).

Step4: Analyze triangle \(D\)

Vertical side \(= 3\) units, horizontal side \(= 2\) units. Hypotenuse: \(3^{2}+2^{2}=13\), \(c=\sqrt{13}\). Same size and shape as \(A\) (translation / rotation / reflection possible).

Step5: Analyze triangle \(E\)

Vertical side \(= 3\) units, horizontal side \(= 1\) unit. Sizes are different from \(A\).

Answer:

Triangle \(C\), Triangle \(D\)