332354 + Interview Questions in Secondary School in Math

1.	State and prove Mid-point Theroem
Answer» OVERVIEW Geometry is one AMONG the significant and essential branches of mathematics. This field deals with the geometrical problems and figures which are based on their properties. One of the important theorems in the field of geometry that deals with the properties of triangles are called the Mid- Point Theorem. The theory of MIDPOINT theorem is used in coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. Both the ‘x’ and the ‘y’ coordinates must be known for solving an equation using this theorem. The Mid- Point Theorem is also useful in the fields of calculus and algebra. MidPoint Theorem Statement The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.” MidPoint Theorem Proof If the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides. Consider the triangle ABC, as shown in the above figure, Let E and D be the midpoints of the sides AC and AB. Then the line DE is said to be parallel to the side BC, WHEREAS the side DE is half of the side BC; i.e. DE∥BC DE = (1/2 * BC). Now consider the below figure, Mid- Point Theorem Construction- Extend the line segment DE and produce it to F such that, EF = DE. In triangle ADE and CFE, EC = AE —– (given) ∠CEF = ∠AED (vertically opposite angles) EF = DE (by construction) By SAS congruence criterion, △ CFE ≅ △ ADE Therefore, ∠CFE = ∠ADE {by c.p.c.t.} ∠FCE= ∠DAE {by c.p.c.t.} and CF = AD {by c.p.c.t.} ∠CFE and ∠ADE are the alternate interior angles. Assume CF and AB as two lines which are intersected by the transversal DF. In a similar way, ∠FCE and ∠DAE are the alternate interior angles. Assume CF and AB are the two lines which are intersected by the transversal AC. Therefore, CF ∥ AB So, CF ∥ BD and CF = BD {since BD = AD, it is proved that CF = AD} Thus, BDFC forms a PARALLELOGRAM. By the properties of a parallelogram, we can write BC ∥ DF and BC = DF BC ∥ DE and DE = (1/2 * BC). Hence, the midpoint theorem is proved ⚕️ NONEXISTENT⚕️

1.

State and prove Mid-point Theroem

Answer»

OVERVIEW

Geometry is one AMONG the significant and essential branches of mathematics. This field deals with the geometrical problems and figures which are based on their properties. One of the important theorems in the field of geometry that deals with the properties of triangles are called the Mid- Point Theorem.

The theory of MIDPOINT theorem is used in coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. Both the ‘x’ and the ‘y’ coordinates must be known for solving an equation using this theorem. The Mid- Point Theorem is also useful in the fields of calculus and algebra.

MidPoint Theorem Statement

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

MidPoint Theorem Proof

If the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides.

Consider the triangle ABC, as shown in the above figure,

Let E and D be the midpoints of the sides AC and AB. Then the line DE is said to be parallel to the side BC, WHEREAS the side DE is half of the side BC; i.e.

DE∥BC

DE = (1/2 * BC).

Now consider the below figure,

Mid- Point Theorem

Construction- Extend the line segment DE and produce it to F such that, EF = DE.

In triangle ADE and CFE,

EC = AE —– (given)

∠CEF = ∠AED (vertically opposite angles)

EF = DE (by construction)

By SAS congruence criterion,

△ CFE ≅ △ ADE

Therefore,

∠CFE = ∠ADE {by c.p.c.t.}

∠FCE= ∠DAE {by c.p.c.t.}

and CF = AD {by c.p.c.t.}

∠CFE and ∠ADE are the alternate interior angles.

Assume CF and AB as two lines which are intersected by the transversal DF.

In a similar way, ∠FCE and ∠DAE are the alternate interior angles.

Assume CF and AB are the two lines which are intersected by the transversal AC.

Therefore, CF ∥ AB

So, CF ∥ BD

and CF = BD {since BD = AD, it is proved that CF = AD}

Thus, BDFC forms a PARALLELOGRAM.

By the properties of a parallelogram, we can write

BC ∥ DF

and BC = DF

BC ∥ DE

and DE = (1/2 * BC).

Hence, the midpoint theorem is proved

5.	Please solve that question
Answer» Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative (commonly CARRIED by protons and electrons respectively). Like charges repel each other and unlike charges attract each other. An OBJECT with an absence of NET charge is referred to as neutral. Early knowledge of how charged substances interact is now called CLASSICAL electrodynamics, and is still accurate for problems that do not require consideration of quantum EFFECTS.

6.	Show that the points A(0,0),B(3,0),C(4,1),and D(1,1) from a palleogram
Answer» gtgugfuin STATION to and

29.	The cost of a pencils is 25 p more than the cost of a eraser if cost of a 8 pencils and 10 erasers is rs12.80 find the cost of each
Answer» $\begin{array}{1 1} ERASER= 60\;cents; pencil =85\; cents \\ eraser= 85 \;cents ; Pencil =60\; cents \\ eraser= \$ 85;Pencil =\$ 60 \\ None \;of\;these \END{array} $

30.	It is given triangleABC is congruent to triangle DEF is it true that AB =EF
Answer» 1 Answer. No, AB and EF are not CORRESPONDING SIDES in triangles ABC and DEF.

40.	125 ग्राम ऑफ न्यू हॉट प्रोवाइड 4.5 ग्राम ऑफ इन हाउ मेनी ग्राम ऑफ प्रोटीन 10 हंड्रेड ग्राम ऑफ यू हार्ट प्रोवाइड सलूशन
Answer» 5 High-Protein FOODS: हम आपको बताते हैं ऐसे 5 फूड्स के बारे में जिनमें अंड़े से ज्यादा प्रोटीन होता है. तो अब अंडा पसंद न होने पर इसे खाने की कोई जरूरत नहीं. या फिर अगर आप सिर्फ अंडा खा-खाकर बोर हो चुके हैं, तो इसके और स्वादिष्ट विकल्पों पर डालते हैं एक नजर...

44.	1. Rationalise the denominator i)1----√2ii)1 -----√7-2
Answer» *ANSWER ----------> REFERRED to the IMAGE...*

49.	Which term of the GP 7, 21, 63....1701?
Answer» SOLUTION: By USING GEOMETRIC SEQUENCE: Let a₁ =7, a₂ = 21, a₃ = 63, and a₁₀ be the 10TH term in the sequence

25.	Plz give me the right answer.
Answer»

26.	Using Identities : 78x 82
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Show that the points A(0,0),B(3,0),C(4,1),and D(1,1) from a palleogram

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Show that:cos²(45° + ø) + cos²(45° - ø)/tan(60° + ø) tan(30° - ø) = 1

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