Question

1. are the following two figures similar or congruent? similar congruent

Explanation:

Step1: Recall definitions

Similar figures have same - shape (proportional side - lengths and equal angles), congruent figures have same shape and size (equal side - lengths and equal angles).

Step2: Analyze side - lengths

Count the grid units for side - lengths of the two triangles. For the purple triangle with vertices \(G(-4,4)\), \(H(-4,2)\), \(I(-1,2)\), side \(GH = 2\) units and \(HI=3\) units. For the pink triangle with vertices \(N(1, - 4)\), \(O(5,-4)\), \(P(5,2)\), side \(NO = 4\) units and \(OP = 6\) units. The ratios of corresponding sides are \(\frac{NO}{GH}=\frac{4}{2}=2\) and \(\frac{OP}{HI}=\frac{6}{3}=2\). The angles of both right - angled triangles are \(90^{\circ}\) and the other non - right angles are equal due to similar slope of the non - vertical and non - horizontal sides.

Answer:

similar