SSS Similarity

Q. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of $\Delta$PQR. Show that $\Delta$ABM $\cong$ $\Delta$PQN

Q.

State true or false:

Triangles shown below are similar.

1. True

2. False

Q. Question 3 (i)
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABM\cong \Delta PQN$

Q. 17. ABC is a right triangle such that AB=AC and bisector of angle C intersects the side AB at D. Prove that AC+AD=BC

Q. Question 6
If in two $\Delta DEFand\Delta PQR,\angle D=\angle Qand\angle R=\angle E$, then which of the following is not true?

(A) $\frac{EF}{PR}=\frac{DF}{PQ}$
(B) $\frac{DE}{PQ}=\frac{EF}{RP}$
(C) $\frac{DE}{QR}=\frac{DF}{PQ}$
​​​​​​(D) $\frac{EF}{RP}=\frac{DE}{QR}$

Q. Question 3 (ii)
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABC\cong \Delta PQR$

Q. In the given figure, if AD = BC and AD || BC, then .

1. AB = AD
2. AB = DC
3. AC = BC

Q. (H): In }△ ABC, D is mid point of }\overline{BC} . }E is foot of perpendicular } from }C on external angle bisector of }\angle BAC . prove 2 DE = } AB+ AC

Q. In $\Delta ABC$, AB = AC and AD is the median. $\Delta ADB$ and $\Delta ADC$ are

1. similar by AA similarity criterion
2. similar by SAS similarity criterion
3. similar by SSS similarity criterion
4. not similar

Q.

In the given figure, $AB$ and $DE$ are perpendicular to $BC$.

Prove that $\Delta ABC~\Delta DEC$, If $AB=6cm,DE=4cm,AC=15cm$, then calculate $CD$, Find the ratio of $Area\left(\Delta ABC\right):Area\left(\Delta DEC\right)$.

Q. Let ABC be an acute angled triangle. Let D and F be mid points of BC and AB respectively. Let perpendiculars from F to AC and perpendicular from B on BC meet at N . Prove that ND is the circumradius of AB

Q. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABM\cong \Delta PQN$

Q. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABM\cong \Delta PQN$

Q. Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:
$\Delta ABM\cong \Delta PQN$

Q. In fig, $ABC$ and $ABD$ are two triangles on the same base $AB$. If line-segment $CD$ is bisected by $AB$ at $O$, show that $ar\left(ABC\right)=ar\left(ABD\right)$.

Q. 2. In a triangle ABC, prove that AB+BC+AC>2AB

Q. in △ ABC. prove that AB+BC+CA>2AB

Q. In the following figure, side BA of triangle ABC is extended upto D, and DE || CB. If \(\angle ADE = 70^\circ\) and \(\angle ACB = 40^\circ\), find the measure of \(\angle BAC.\)

Q. Which of the following statements are correct for the correspondence between the vertices of two triangles?
(P) The area of two similar triangles is equal.
(Q) The corresponding angles of both similar triangles are having same proportion.
(R) The corresponding sides of both similar triangles are having same proportion.
(S) The corresponding sides of both similar triangles are congruent.

1. Only statement R is correct.
2. Statement Q and S are correct.
3. Statement P, Q and R are correct.
4. Statement Q and R are correct.

Q. $\text{Observe the given triangles and find the}\text{value of}\angle P.$

Q. $AB=10.8cm,AD=4.5cm,AC=4.8cm$ and $AE=2.8cm$

1. Yes
2. No
3. Can't say
4. Ambiguos