The fourth question on page 135 of the eighth grade mathematics book published by Beijing Normal University puts two identical isosceles right-angled triangles as shown in the figure, assuming that all points and lines in the figure are in the same plane.

Answer the following questions:

(1) How many triangles are there in the graph? Write them out one by one;

(2) Is there a similar triangle (excluding congruence) in the diagram? If there are, write them down one by one.

[Resolution]: (1) Look at △ABC first, * * has six triangles, plus △AFG, * * seven triangles; (2) Because ∠ DAE = ∠ B = ∠ C = 45, ∠ ADE = ∠ B+∠1= 45+∠1= ∠ BAE, the same is true.

(1) * * * There are seven triangles, which are:

△ABD△ABE△ABC△ADE△ADC△AEC△AFG .

(2) similar triangle, they are:

△ADE∽△BAE，

∠B=∠DAE, ∠ADE is a common angle, so △ADE∽△BAE.

△BAE∽△CDA，

∠DAE=∠B=∠C=45，

∠ADE =∠b+∠ 1 = 45+∠ 1 =∠BAE，

Using the same method ∠ AED = ∠ CAD, you can get △BAE∽△CDA.

△ADE∽△CDA (or △ADE∽△BAE∽△CDA)

∠C=∠ADE, ∠ADC is a common angle, so △ADE∽△CDA.