Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. the diagram represents the design of a triangular - shaped photo frame. match the segments and angles to the descriptions. (diagram: triangle abc with ∠a = 82°, ∠b = 58°. tiles: ∠c, ∠b, ac, ∠a, ab, bc. boxes: shortest side, longest side, smallest angle, largest angle)

Explanation:

Step1: 计算∠C的度数

三角形内角和为\(180^\circ\)，已知\(\angle A = 82^\circ\)，\(\angle B = 58^\circ\)，则\(\angle C = 180^\circ - 82^\circ - 58^\circ = 40^\circ\)。

Step2: 比较角的大小

\(\angle C = 40^\circ\)，\(\angle B = 58^\circ\)，\(\angle A = 82^\circ\)，所以\(\angle C < \angle B < \angle A\)，即最小角为\(\angle C\)，最大角为\(\angle A\)。

Step3: 根据大角对大边，小角对小边

因为\(\angle C\)最小，所以对边\(AB\)最短；\(\angle A\)最大，所以对边\(BC\)最长。

Answer:

shortest side → AB
longest side → BC
smallest angle → ∠C
largest angle → ∠A