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Seek the answer to the first chapter review questions in the second volume of the eighth grade (Beijing Normal University Edition)!
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.