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Solve the problems. Write the complete proof.


ONLY HAVE TO PROVE HOW BD IS PERPENDICULAR TO AC!

Solve The Problems Write The Complete Proof ONLY HAVE TO PROVE HOW BD IS PERPENDICULAR TO AC class=

Sagot :

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. An isosceles triangle is one with two equal-length sides.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔBAD and ΔBDC,

m∠ADB = m∠CDB {Given}

BD = BD {Common side in two triangles}

AD ≅ DC {Given}

Using the ASA postulate the two triangles are congruent. Therefore,

m∠BAD= m∠BCD.........equation 1

m∠ABD= m∠CBD

In ΔADC, AD ≅ DC {Given}, therefore, the triangle is an isosceles triangle. Thus,

m∠DAE = m∠DCE.......equation 2

Adding two of the equation 1 and 2,

m∠BAD + m∠DAE = m∠DCE + m∠BCD

∠BAC = ∠BCA

Since in ΔABC, ∠BAC = ∠BCA therefore, the triangle is an isosceles triangle, thus, AB = BC,

BE is the common side between ΔAEB and ΔCEB

Also, m∠ABD= m∠CBD

Therefore, ΔAEB ≅ ΔCEB

Now as ΔAEB ≅ ΔCEB, therefore, AE=EC,

Thus, BE is the median of the isosceles triangle ABC, and for an isosceles triangle, the median opposite to the non-common sides is the perpendicular bisector to the opposite side.

Hence, BD⊥AC.

Learn more about Triangle:

https://brainly.com/question/2773823

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