Question

prove that the line segment joining tge midpoint of the sides of a rectangle is a rhombus

Answer 1

Step-by-step explanation:

Let the given rectangle be ABCD and the mid-points of AB , BC  

CD and AD respectively be P, Q, R and S .  

NOW join the diagonals AC and BD .  

using mid-point theorem;  

In ∆ ABC, PQ // AC and PQ = (1/2) AC - - - - - - - -(i)  

In ∆ ADC, RS // AC and RS = (1/2) AC - - - - - - - -(ii)  

In ∆ BCD, QR // BD and PQ = (1/2) BD - - - - - - - -(iii)  

In ∆ ABD, PS // BD and PS = (1/2) BD - - - - - - - -(iv)  

But diagonals (AC & BD) are equal caz its a rectangle.  

therefore, from (i) , (ii) , (iii) & (iv), PQ = QR = RS = PS  

so, PQRS is a rhombus.

i hope it will helps you mate

Answer 2

Answer:

A galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.[1][2] The word is derived from the Greek galaxias (γαλαξίας), literally "milky", a reference to the Milky Way. Galaxies range in size from dwarfs with just a few hundred million (108) stars to giants with one hundred trillion (1014) stars,[3] each orbiting its galaxy's center of mass.

Galaxies are categorized according to their visual morphology as elliptical,[4] spiral, or irregular.[5] Many are thought to have supermassive black holes at their centers. The Milky Way's central black hole, known as Sagittarius A*, has a mass four million times greater than the Sun.[6] As of March 2016, GN-z11 is the oldest and most distant galaxy observed. It has a comoving distance of 32 billion light-years from Earth, and is seen as it existed just 400 million years after the Big Bang.

In 2021, data from NASA's New Horizons space probe was used to revise the previous estimate to roughly 200 billion galaxies (2×1011),[7] which followed a 2016 estimate that there were two trillion (2×1012) or more[8][9] galaxies in the observable universe, overall, and as many as an estimated 1×1024 stars[10][11] (more stars than all the grains of sand on all beaches of the planet Earth).[12] Most of the galaxies are 1,000 to 100,000 parsecs in diameter (approximately 3,000 to 300,000 light years) and are separated by distances on the order of millions of parsecs (or megaparsecs). For comparison, the Milky Way has a diameter of at least 30,000 parsecs (100,000 ly) and is separated from the Andromeda Galaxy, its nearest large neighbor, by 780,000 parsecs (2.5 million ly.)

Step-by-step explanation: