As shown in the figure, in square ABCD, G is any point on BC, AE is vertical DG, CF is vertical Gd, and the perpendicular feet are e and f respectively

As shown in the figure, in square ABCD, G is any point on BC, AE is vertical DG, CF is vertical Gd, and the perpendicular feet are e and f respectively

(1) Find out a pair of congruent triangles in the figure and explain the reason; (2) explain AE = FC + EF. (1) △ AED is equal to △ DFC. Prove: ∵ quadrilateral ABCD is a square ∵ ad = DC ∵ ADC = 90 °

In the parallelogram ABCD, EF is the point AE = CF on bcab and intersects g to prove DG bisection ∠ AGC
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Connect de and DF, and make DM and DN of AE and FC through D. m and N are perpendicular triangles. The area of ADE = half of the area of parallelogram, and the area of triangle DFC = half of the area of parallelogram. So the area of triangle ade = the area of triangle DFC. So AE times DM = FC times DN. From AE = CF, DM = DN and D

As shown in the figure, in square ABCD, e and F are two points on the edge of AB and BC, and EF = AE + FC, DG ⊥ EF is in G, proving: DG = da

Extend BC to H point, make ch = AE, connect De, DF, from AE = ch, ∠ DAE = ∠ DCH, ad = CD, get: △ AED ≌ △ CHD, ≌ de = DH, and ≌ FH = Fe, DF = DF, de = DH, ≌ △ def ≌ △ DFH, ≂ DG is the height of EF side in △ def, DC is the height of HF side in △ DHF, and EF, HF are the corresponding sides of congruent triangles, ≌ DG = DC, and ≌ square are equal, ≌ DG = da

As shown in the figure, the quadrilateral abed and AFCD are parallelograms with an area of 36 square centimeters. The triangle AOD is a right triangle. Ao, do and AD are 3, 4 and 5 centimeters long respectively. Calculate the area of quadrilateral ABCD

Because de × 3 = 36, then de = 12 cm, OE = 12-4 = 8 cm, similarly: AF × 4 = 36, then AF = 9 cm, of = 9-3 = 6 cm, so the area of quadrilateral ABCD is: 36 × 2 + 8 × 6 △ 2-3 × 4 △ 2, = 72 + 24-6, = 90 (square cm); answer: the area of quadrilateral ABCD is 90 square cm