(B) The statement is $False$.According to the $SAS$ (Side-Angle-Side) similarity criterion,two triangles are similar if one angle of one triangle is e

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(B) The statement is $False$.According to the $SAS$ (Side-Angle-Side) similarity criterion,two triangles are similar if one angle of one triangle is equal to one angle of the other triangle and the sides including these angles are proportional.In the given statement,the two sides are proportional,but they are not necessarily the sides that include the equal angle. Therefore,the condition for $SAS$ similarity is not satisfied,and the triangles are not necessarily similar.

Class 10 Mathematics Triangles Mix Examples - Triangles

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Is it true to say that if in two triangles,an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle,then the triangles are similar? Give reasons for your answer.

A
Yes
B
No
C
Cannot be determined
D
Depends on the triangle type

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Class 10

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Triangles

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Mix Examples - Triangles

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 8$,$QS = 5.6$ and $QR = 12.6$,find $PR$.

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In $\square ABCD$,$P \in \overline{AB}$,$Q \in \overline{BC}$,$R \in \overline{CD}$,and $S \in \overline{DA}$ such that $\frac{AP}{PB} = \frac{AS}{SD}$ and $\frac{CB}{QB} = \frac{CR}{RD}$. Prove that $\overline{PS} \parallel \overline{QR}$.

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In $\Delta PQR$,$m\angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $PQ = 8$ and $QR = 6$,find the area of $\Delta QMR$.

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In quadrilateral $ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $OA = 3x - 19$,$OB = x - 4$,$OC = x - 3$,and $OD = 4$,find the value of $x$.

Medium

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In $\Delta XYZ$,$m\angle Y = 90^{\circ}$. If $XY = a^{2} - b^{2}$ and $YZ = 2ab$,find $XZ$ (where $a > b > 0$).

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Is it true to say that if in two triangles,an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle,then the triangles are similar? Give reasons for your answer.

Similar Questions

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 8$,$QS = 5.6$ and $QR = 12.6$,find $PR$.

In $\square ABCD$,$P \in \overline{AB}$,$Q \in \overline{BC}$,$R \in \overline{CD}$,and $S \in \overline{DA}$ such that $\frac{AP}{PB} = \frac{AS}{SD}$ and $\frac{CB}{QB} = \frac{CR}{RD}$. Prove that $\overline{PS} \parallel \overline{QR}$.

In $\Delta PQR$,$m\angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $PQ = 8$ and $QR = 6$,find the area of $\Delta QMR$.

In quadrilateral $ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{O\}$. If $OA = 3x - 19$,$OB = x - 4$,$OC = x - 3$,and $OD = 4$,find the value of $x$.

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$. If $XY = a^{2} - b^{2}$ and $YZ = 2ab$,find $XZ$ (where $a > b > 0$).

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