Im stuck on a few questions of my maths assignment, quite a few actually. Please help someone!!??!

Q2. Simplify (n-1)C2+nC2 (Its a combination thing). State any restrictions that must be placed on n

Q7. Heres how to draw it: Draw a scalene triangle, and label the bottom right angle A, and clockwise add B and C to other angles. Now on BA there is a midpoint T. Connect T to C. ALso, on BC there is a point P. Connect A to P. Now AP intersects TC at E. AE is perpendicular to CT. TC bisects angle C. Connect E with M.

i) Prove triangle ACE is congruent to triangle PCE ( I cant find a third reason, only two)

ii) Explain why AE= EP (Matching sides congruent triangles from i)

iii) Hence prove EM is parallel to PB

This question is damn easy lolz I just cant seem to get the right result, how stupid of me -_-

Q15. Here's how to draw diagram: Draw a right angled triangle ABC, labelled clockwise from A at the top. Make C face west of the page. Now with AB as a common side, draw a reflection of the triangle, except extend the hypotenuse and AB further so A reaches to D, which is past B, and the hypotenuse reaches to E, such that the formed angle of ADE =90 degrees. Now connect C to E. CE intersects BD at F. Overall, triangle ABC is similar to triangle AD, and AB=a units. The ratio of similarity of AB:AD is k:l

Here are the questions:

a) Prove triangle FBC is similar to triangle FDE

b) find the ratio of the lengths BF to FD

c) SHow that FD=(al(l-k))/(k(l+k))

d) Given AB:AD=2:3, and FD is an integer, find the possible values of A.

Q16.

a) Prove tan(a+b+c)=(tana+tanb+tanc-tan(a)tan(b)tan(c))/(1-tanatanb-tanatanc-tanbtanc)

i)If a, b and c are the angles of a triangle, explain why tana+tanb+tanc-tanatanbtanc=0

b)Given tana/2=tanba/3=tanc/4=k, show that k=sqrt(6)/4

c) Hence find the size of a in degrees and minutes

SORRY ITS SO BIG! Its just super hard and im a bit confused. PLease help with working out!

Q2. Simplify (n-1)C2+nC2 (Its a combination thing). State any restrictions that must be placed on n

Q7. Heres how to draw it: Draw a scalene triangle, and label the bottom right angle A, and clockwise add B and C to other angles. Now on BA there is a midpoint T. Connect T to C. ALso, on BC there is a point P. Connect A to P. Now AP intersects TC at E. AE is perpendicular to CT. TC bisects angle C. Connect E with M.

i) Prove triangle ACE is congruent to triangle PCE ( I cant find a third reason, only two)

ii) Explain why AE= EP (Matching sides congruent triangles from i)

iii) Hence prove EM is parallel to PB

This question is damn easy lolz I just cant seem to get the right result, how stupid of me -_-

Q15. Here's how to draw diagram: Draw a right angled triangle ABC, labelled clockwise from A at the top. Make C face west of the page. Now with AB as a common side, draw a reflection of the triangle, except extend the hypotenuse and AB further so A reaches to D, which is past B, and the hypotenuse reaches to E, such that the formed angle of ADE =90 degrees. Now connect C to E. CE intersects BD at F. Overall, triangle ABC is similar to triangle AD, and AB=a units. The ratio of similarity of AB:AD is k:l

Here are the questions:

a) Prove triangle FBC is similar to triangle FDE

b) find the ratio of the lengths BF to FD

c) SHow that FD=(al(l-k))/(k(l+k))

d) Given AB:AD=2:3, and FD is an integer, find the possible values of A.

Q16.

a) Prove tan(a+b+c)=(tana+tanb+tanc-tan(a)tan(b)tan(c))/(1-tanatanb-tanatanc-tanbtanc)

i)If a, b and c are the angles of a triangle, explain why tana+tanb+tanc-tanatanbtanc=0

b)Given tana/2=tanba/3=tanc/4=k, show that k=sqrt(6)/4

c) Hence find the size of a in degrees and minutes

SORRY ITS SO BIG! Its just super hard and im a bit confused. PLease help with working out!

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