Question

in the figure ad// bc x and y are midpoints of ab and CD show that xy parallel to ad and bc and xy is equal to 1/2(ad+bc)​

Answer 1

Given :-

• AD || BC .
• X and Y are mid points of AB and CD .

To Prove :-

• XY || AD and XY || BC .
• XY = (1/2)[AD + BC]

Answer :-

In ∆ZBC , we have given that , AD || BC .

so,

→ ZA / AB = ZD / DC { By BPT .}

since, X and Y are mid points of AB and CD .

→ ZA / 2*AX = ZD / 2*DY

→ ZA / AX = ZD / DY

then,

→ AD || XY { By converse of BPT. } (Proved)

therefore,

→ XY || BC { Lines parallel to same line are parallel to each other. }

now, in ∆ABC, we have,

→ AX = XB { given that X is mid - point of AB. }

→ XP || BC { as XY || BC .}

so,

→ AP = PC { By converse of mid point theorem. }

then,

→ XP = (1/2)(BC) { By mid point theorem. } ---------- Eqn.(1)

similarly, in ∆ACD,

→ PY || AD

→ DY = YC

so,

→ PY = (1/2)(AD) ----------- Eqn.(2)

adding Eqn.(1) and Eqn.(2),

→ XP + PY = (1/2)BC + (1/2)AD

→ XY = (1/2)[BC + AD]

→ XY = (1/2)[AD + BC] (Proved.)

Learn more :-

in triangle ABC seg DE parallel side BC. If 2 area of triangle ADE = area of quadrilateral DBCE find AB : AD show that B...

https://brainly.in/question/15942930

2) In ∆ABC seg MN || side AC, seg MN divides ∆ABC into two parts of equal area. Determine the value of AM / AB

https://brainly.in/question/37634605

Answer 2

Answer:

THE UPPER ANSWER IS ABSOLUTELY CORRECT,IF U NEED SHORT,CONVEY ME I WILL EXPOSE U. , OR IF U NEED STILL BROAD. CONVEY ME, I WILL RESPOND. TAKE CARE STAY SAFE, READ WELL