In ABC, D is a point on the edge of AC, DE AB is at E, and the extension line of BC is at F after ED

Solution: cd=cf

cdf=∠cfd

ade=∠cdf

ade=∠cfd

ab⊥ef∠b+∠cfd=90°

a+∠ade=90°

ade=∠cfd

a=∠bac=bc

ABC is an isosceles triangle.

cd=cfcdf=∠cfd

ade=∠cdf

ade=∠cfd

ab⊥ef∠b+∠cfd=90°

a+∠ade=90°

ade=∠cfd

a=∠bac=bc

ABC is an isosceles triangle.

b=90°-∠f=90°-30°=60°

The isosceles triangle ABC is a regular triangle.

I'm glad to answer your questions and wish you progress in your studies! The Learning Guide team will answer the questions for you.

If you don't understand, you can ask! If you approve of mine.

Please click the [Select as satisfied] button below, thank you!

Since cd=cf

So cdf= f

So a=90°- cdf=90°- f= b, so ac=bc

2) If there is f=30° again

Then a= b=90°- f=60° (with the first question) so c=60°

So ab=ac=bcSo, abc is an equilateral triangle and don't understand it, welcome to ask, if it helps, thank you!

Solution: (1) CDF= CF is obtained by CD=CFD, and the extension line of De AB in E, Ed crosses the extension line of BC in F

This gives ade= cdf, so ade= cfd, aed+ ade=90°, cfd= bfd, cfd+ ebf=90°, and ade= cfd

So ead= ebf, i.e. bac= abc, so abc is an isosceles triangle.

2) If cd=cf and f=30°

The extension of de ab to e, ed to the extension of bc to f

CDF= ADE= F=30°, so EAD= EBF=90°-30°=60°, i.e. BAC= ABC=60°

Whereas, BCA=180°-(EAD+EBF)=180°-(60°+60°)=60°

So abc is an equilateral triangle.

Because cd=cf, cdf is an isosceles triangle.

So: f= cdf= ade

Because: de ab

So: triangle aed.

a+∠ade=90

Triangle feb.

f+∠b=90

So: a+ ade= f+ b

Again: f= ade

So: a= b

ABC is an isosceles triangle.

Proof: de ab in e

f+∠b=∠eda+∠a=90°

cd=cf∠f=∠cdf

Whereas cdf= eda

f=∠eda

And f+ b= eda+ a=

b= a abc is an isosceles triangle.

1: Because AH is parallel to BE

So angle h = angle e

The angle ADH and the angle CDE are diagonal so they are equal.

Therefore, the triangle adh is similar to the triangle cde, and the triangle d is the midpoint of ac, so ad=cd

So the triangle adh and the triangle cde are congruent triangles, so ah=ce

2: Because AH is parallel to BE

So horn bah = horn abe

The angle AFH and the angle BFE are diagonal so they are equal.

So AFH is similar to BFE.

Because ab=4af

So bf = 3af

So HF=3EF

eh=8=4hf

hf = 2 because the triangle adh and the triangle cde are congruent triangles, so hd = de

hd=4df=4-hf=4-2=2

1: F= CDF is deduced from cd=cf

There is also an equal inference of the apex angles ade= cdf

So f= ade, and then there are both aed and bef are right angles, and a= b can be deduced from the similarity of triangles or the inner angles and 180 degrees

This is an isosceles triangle.

2. If the isosceles triangle abc is equilateral, only one of them b=60 degrees, which should be in the right-angled bef.

f = 90- b = 30 degrees.

(1) Because cd=cf, the triangle cdf is an isosceles triangle.

So cdf= f

And because cdf = ade (to the apex angle).

All ade= f.

and because of de ab, then aed= feb=90

So a=180- aed-ade

b=180-∠feb-∠f

So: a= b

The triangle ABC is an isosceles triangle.

2) When f=30, acb= cdf+ f=60 a= b= acb=60

The triangle ABC is an equilateral triangle.

No diagram, no diagram, no diagram. Swollen write??