Two triangles are said to be congruent if all three sides and three angles of one triangle is equal to three sides and three angles of the other triangle.

From the question:

BD ≅ BD (reflexive property of equality)

Since BD is the angle bisector of ∠ABC, hence ∠ABD = ∠CBD

∠ABD = 2x + y, ∠CBD = 14 + y. Therefore:

2x + y = 14 + y

2x = 14 + y - y

2x = 14

x = 14 / 2

x = 7

Also, ∠BAD = ∠BCD = 90° (right angled triangle)

Since ∠BAD = ∠BCD, BD ≅ BD and ∠ABD = ∠CBD, therefore ΔABD is congruent to ΔCBD by angle-angle-side congruence theorem.

The angle-angle-side congruence theorem states that if two angles and one side of one triangle is equal to two angles and one side of another triangle the both triangles are congruent.

ΔABD is congruent to ΔCBD, therefore AD = CD

5x - y = x + 13y

13y + y = 5x - x

14y = 4x

14y = 4(7)

y = 4(7) / 14

y = 2

7 0

2 years ago

Write a short imaginary letter to your congressional leader expressing your support for aid to Africa (or your position against

Serggg [28]

Supporting points are:
Help the disadvantaged,support the underdeveloped nations humanitarian departments such as health and security,help integrate the people into the global economy, especially through educational initiative.It is in line with the moral majority, and christian doctrines of humanity.Can help eradicate human rights abuses as aid is tied to such demands

AgainstMost of the funds get into a few african elites hands anyway Redirecting tax payers money into other nation is morally wrong.It defeats the essence of rationality, as the country gets little benefit by giving out the aid.

8 0

2 years ago

Read 2 more answers

What is the name of the layer of the upper atmosphere about 18.6 miles above earth’s surface that protects us from the effects o

Mila [183]

that would be the Ozone layer

5 0

3 years ago

Which layer contains the most complex animal fossils?

svlad2 [7]

Sedimentary rock layer is the most complex

5 0

2 years ago

Read 2 more answers