Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it. Prove that the medians to the legs of an isosceles triangle are congruent.


What rule did you use to prove triangles congruent? (AAA, SAS, ASA, CannotBeDetermined, SSS)

Could we choose our environment, and were desire in human undertakings synonymous with

endowment, all men would, I suppose, be optimists. Certainly most of us regard happiness as

the proper end of all earthly enterprise. The will to be happy animates alike the philosopher, the

prince and the chimney-sweep. No matter how dull, or how mean, or how wise a man is, he feels

that happiness is his indisputable right.

2 It is curious to observe what different ideals of happiness people cherish, and in what singular

places they look for this well-spring of their life. Many look for it in the hoarding of riches, some

in the pride of power, and others in the achievements of art and literature; a few seek it in the

exploration of their own minds, or in the search for knowledge.

3 Most people measure their happiness in terms of physical pleasure and material possession.

Could they win some visible goal which they have set on the horizon, how happy they would be!

Lacking this gift or that circumstance, they would be miserable. If happiness is to be so

measured, I who cannot hear or see have every reason to sit in a corner with folded hands and

weep. If I am happy in spite of my deprivations, if my happiness is so deep that it is a faith, so

thoughtful that it becomes a philosophy of life,—if, in short, I am an optimist, my testimony to

the creed of optimism is worth hearing

4 Once I knew the depth where no hope was, and darkness lay on the face of all things. Then

love came and set my soul free. Once I knew only darkness and stillness. Now I know hope and

joy. Once I fretted and beat myself against the wall that shut me in. Now I rejoice in the

consciousness that I can think, act and attain heaven. My life was without past or future; death,

the pessimist would say, “a consummation devoutly to be wished.” But a little word from the

fingers of another fell into my hand that clutched at emptiness, and my heart leaped to the

rapture of living. Night fled before the day of thought, and love and joy and hope came up in a

passion of obedience to knowledge. Can anyone who has escaped such captivity, who has felt

the thrill and glory of freedom, be a pessimist?

5 My early experience was thus a leap from bad to good. If I tried, I could not check the

momentum of my first leap out of the dark; to move breast forward is a habit learned suddenly

at that first moment of release and rush into the light. With the first word I used intelligently, I

learned to live, to think, to hope. Darkness cannot shut me in again. I have had a glimpse of the

shore, and can now live by the hope of reaching it.

6 So my optimism is no mild and unreasoning satisfaction. A poet once said I must be happy

because I did not see the bare, cold present, but lived in a beautiful dream. I do live in a

beautiful dream; but that dream is the actual, the present,—not cold, but warm; not bare, but

furnished with a thousand blessings. The very evil which the poet supposed would be a cruel

6) Read the last sentence from the text.

Only by contact with evil could I have learned to feel by contrast the beauty of truth and love and goodness.

Explain how Helen Keller develops this idea in the text. Use specific details to

support your answer.

BD=5, AB=15

Step-by-step explanation:

Because AB = AC, AC =15, SO AB = 15

Because Δ DAB ≅ Δ DAC, So BD = DC =5

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it