给出该问题的详细解答过程---**Question Stem:**
16. 如图, 点 C, D 在线段 AB 上 (点 C 在点 A, D 之间), 分别以 AD, BC 为边向同侧作等边三角形 ADE 与等边三角形 CBF, 边长分别为 a, b. CF 与 DE 交于点 H, 延长 AE, BF 交于点 G, AG 长为 c.
**Sub-questions:**
(1) 若四边形 EHFC 的周长与 △CDH 的周长相等, 则 a, b, c 之间的等量关系为 _______.
(2) 若四边形 EHFC 的面积与 △CDH 的面积相等, 则 a, b, c 之间的等量关系为 _______.
**Chart/Diagram Description:**
* **Type:** Geometric figure composed of points, line segments, and triangles.
* **Main Elements:**
* **Points:**
* A, C, D, B are four distinct points collinear on a horizontal line segment (implicitly AB). Point C is positioned between A and D.
* E, F, H, G are points located above the line segment AB.
* **Line Segments:**
* A horizontal base line segment AB.
* Triangle ADE is an equilateral triangle with sides AD, DE, and EA. Its side length is denoted by 'a', meaning AD = DE = EA = a.
* Triangle CBF is an equilateral triangle with sides CB, BF, and FC. Its side length is denoted by 'b', meaning CB = BF = FC = b.
* Line segment CF intersects line segment DE at point H.
* Line segment AE is extended upwards to point G.
* Line segment BF is extended upwards to point G.
* Line segment EF connects points E and F.
* Line segment GH connects points G and H.
* Line segment CD is a portion of the base AB.
* **Shapes:**
* Equilateral triangle ADE.
* Equilateral triangle CBF.
* Quadrilateral EHFC, which is shown shaded with a light gray pattern. Its vertices are E, H, F, C.
* Triangle CDH, with vertices C, D, H.
* Triangle ABG, a larger triangle formed by the base AB and the extended lines AE and BF meeting at G.
* **Labels and Annotations:**
* The length of side AD (and DE, EA) is labeled 'a'.
* The length of side BC (and BF, FC) is labeled 'b'.
* The length of line segment AG is labeled 'c'.
* **Relative Position and Direction:**
* Points A, C, D, B are ordered sequentially from left to right on the base line.
* Both equilateral triangles ADE and CBF are constructed on the same side (upwards in the drawing) of the base line AB.
* Point H is the intersection point located within the quadrilateral ABFE.
* Point G is the common intersection point of the extended line segments AE and BF, located above and between E and F.