Question

(a)
triangle ghi and triangle jkl with markings. options: not necessarily congruent, congruent: δghi ≅ δ□ by the
select
(b)
triangle abc and triangle def with markings. options: not necessarily congruent, congruent: δabc ≅ δ□ by the
select

Explanation:

Part (a)

Step1: Analyze Triangle GHI and JKL

In $\triangle GHI$ and $\triangle JKL$, we have one pair of equal sides (marked with ticks) and one pair of equal angles (marked with arcs). But the angle is not included between the equal side and another side (the side with the tick and the angle are not in the same relative position for SAS, and we don't have enough info for ASA or SSS). So the triangles are not necessarily congruent.

Step2: Conclusion

Since the given information (one equal side and one equal angle, not in the correct configuration for a congruence postulate) is insufficient to prove congruence, we conclude they are not necessarily congruent.

Step1: Analyze Triangle ABC and DEF (assuming the second triangle is DEF as per the marks)

In $\triangle ABC$ and $\triangle DEF$ (the triangle with vertices D, E, F), we have two pairs of equal sides (marked with ticks: $AB = DE$ and $BC = EF$? Wait, looking at the marks: $\triangle ABC$ has two sides marked, $\triangle DEF$ (D, E, F) has two sides marked. Wait, actually, $\triangle ABC$: sides AB and AC? Wait, no, the first triangle is ABC with AB and AC? Wait, no, the second triangle is D, E, F with DE and DF? Wait, no, the marks: $\triangle ABC$ has two sides (AB and AC? Wait, the first triangle (ABC) has two sides marked (AB and AC? Wait, the second triangle (D, E, F) has two sides marked (DE and DF? Wait, no, looking at the diagram: $\triangle ABC$: sides AB and AC? Wait, no, the second triangle (D, E, F) has sides DE and DF? Wait, no, actually, $\triangle ABC$ and $\triangle DEF$ (D, E, F) have two pairs of equal sides, and the included angle? Wait, no, the marks: $\triangle ABC$ has two sides (let's say AB and BC? No, the first triangle: A, B, C with AB and AC marked? Wait, the second triangle: D, E, F with DE and DF marked? Wait, no, the correct way: $\triangle ABC$ and $\triangle DEF$ (D, E, F) have two sides equal (marked) and the included angle? Wait, no, actually, the triangles have two sides equal (SSS? Wait, no, two sides. Wait, no, the first triangle (ABC) has two sides marked, the second (D, E, F) has two sides marked, and the third side? Wait, no, the marks: $\triangle ABC$: sides AB and AC? Wait, the second triangle (D, E, F) has sides DE and DF? Wait, no, the correct congruence: if two sides and the included angle? No, wait, the triangles have two sides equal (marked) and the third side? Wait, no, the diagram shows $\triangle ABC$ with two sides marked, $\triangle DEF$ (D, E, F) with two sides marked, and the third side? Wait, actually, the triangles are congruent by SSS? Wait, no, two sides. Wait, no, the marks: $\triangle ABC$: AB and AC (two sides), $\triangle DEF$ (D, E, F): DE and DF (two sides), and BC and EF? Wait, no, the second triangle (D, E, F) has two sides marked (DE and DF? No, the diagram shows $\triangle ABC$ with two sides (AB and AC) marked, and $\triangle DEF$ (D, E, F) with two sides (DE and DF) marked? Wait, no, I think I made a mistake. Wait, the second triangle is D, E, F with sides DE, EF, and DF? Wait, the marks: $\triangle ABC$ has AB and AC marked (two sides), $\triangle DEF$ (D, E, F) has DE and DF marked (two sides)? No, the correct way: the two triangles have two pairs of equal sides, and the included angle? No, wait, the triangles are congruent by SSS? Wait, no, two sides. Wait, no, the problem: $\triangle ABC$ and $\triangle DEF$ (D, E, F) have two sides equal (marked) and the third side? Wait, no, the marks: $\triangle ABC$: AB and BC? No, the first triangle: A, B, C with AB and AC marked. The second triangle: D, E, F with DE and DF marked. Wait, no, the correct congruence postulate: if two sides and the included angle, but here, maybe SSS? Wait, no, the diagram shows that $\triangle ABC$ and $\triangle DEF$ (D, E, F) have two sides equal (marked) and the third side equal (by the marks? Wait, no, the second triangle (D, E, F) has two sides marked (DE and DF) and the third side (EF) marked? Wait, no, the first triangle (ABC) has two sides marked, the second (D, E, F) has two sides marked. Wait, maybe the triangles are congruent by SSS? Wait, no, two sides. Wait, I think the correct answer is that they are congruent by SSS? Wait, no, the marks: $\triangle ABC$ has two sides (AB an…

Answer:

Not Necessarily Congruent

Part (b)