Polygons

Q. Find the correct option.

1. ∆ABC $\sim$ ∆QPR
2. ∆ABC $\sim$ ∆PQR
3. ∆ABC $\sim$ ∆RPQ
4. ∆ABC $\sim$ ∆RQP

Q. Question 8 (i)
In the given figure, O is a point in the interior of a triangle ABC, OD $\perp$ BC, OE $\perp$ AC and OF $\perp$ AB.
Show that $\left(i\right)O{A}^2+O{B}^2+O{C}^2-O{D}^2-O{E}^2-O{F}^2=A{F}^2+B{D}^2+C{E}^2$

Q. In Figure, $ABC$ is a triangle in which $\angle ABC<{90}^{\circ }$ and $AD\perp BC.$ Prove that $A{C}^2=A{B}^2+B{C}^2-2BC.DB.$

Q. In Figure, $ABC$ is a triangle in which $\angle ABC>{90}^{\circ }$ and $AD\perp CB$ produced.
Prove that $A{C}^2=A{B}^2+B{C}^2+2BC.DB$

Q. Question 2
PQR is a triangle right angled at P and M is a point on QR such that $PM\perp QR$. Show that $P{M}^2=QM\times MR$.

Q. 44. The difference between any two consecutive interior angles of a polygon is 5degree.If the smallest angle is 120degree , find the number of the sides of the polygon.

Q.

Which of the following does not have a diagonal?

1. Triangle

2. Quadrilateral

3. Pentagon

4. None of these

Q. In the given figure, O is a point in the interior of a triangle ABC, OD $\perp$ BC, OE $\perp$ AC and OF $\perp$ AB.
Show that $O{A}^2+O{B}^2+O{C}^2-O{D}^2-O{E}^2-O{F}^2=A{F}^2+B{D}^2+C{E}^2$

Q.

State true/false whether this closed curves are polygon or not.

1. True
2. False

Q.

In a ΔABC, obtuse angled at B, if AD is perpendicular to CB produced, prove that AC = ${AB}^2$ + ${BC}^2$ + 2BC $\times$ BD [4 MARKS]

Q.

$△$ABC is a triangle, right angled at B. BD is a perpendicular to AC as shown. Which of the following is true?

1. $AB\times BC=AD\times DC$

2. ${AD}^2$ + ${CD}^2$ = ${BD}^2$ + ${AB}^2$

3. ${AB}^2$ + ${CD}^2$ = ${BC}^2$ + ${AD}^2$

4. ${AB}^2+{CD}^2={BC}^2\times {AD}^2$

Q. In this triangle $A{D}^2=BD\times CD$

1. True
2. False

Q. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $A{E}^2+B{D}^2=A{B}^2+D{E}^2$.

Q. ABC is an isosceles triangle with AC = BC. If $A{B}^2=2A{C}^2$, prove that ABC is a right triangle.

Q. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $A{E}^2+B{D}^2=A{B}^2+D{E}^2$.

Q. Is a quadrantal angle a coterminal angle also since it has the same initial and terminal ray?

Q. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $A{E}^2+B{D}^2=A{B}^2+D{E}^2$.