Mathematics Part 2 (Geometry) - Solutions Std. X

Vocabulary practice flashcards covering key theorems, properties, tests, and terminology from Maharashtra Board Std. X Mathematics Part 2 (Geometry).

Basic Proportionality Theorem (BPT)

The theorem stating that if a line is parallel to a side of a triangle and intersects the other two sides in two distinct points, then the line divides the two sides in the same proportion ($\frac{AD}{DB} = \frac{AE}{EC}$).

Theorem of Geometric Mean

The theorem stating that in a right-angled triangle, the perpendicular segment drawn from the right angle to the hypotenuse satisfies the relation $QS^2 = PS \times SR$, where $QS$ is perpendicular to hypotenuse $PR$.

Tangent-Radius Property

The geometric principle establishing that a tangent at any point of a circle is perpendicular to the radius through the point of contact ($CA \perp AB$, so $\angle CAB = 90^\circ$).

Tangent-Secant Theorem (Alternate Segment)

The theorem stating that the angle between a tangent and a chord drawn through the point of contact is equal to the angle subtended by the chord in the alternate segment ($\angle NMT = \angle MPN$).

Apollonius Theorem

A theorem relating the lengths of the sides and a median of a triangle, expressed by the formula $PQ^2 + PR^2 = 2PS^2 + 2QS^2$, where $PS$ is the median to side $QR$.

Tangent Segments Theorem

The theorem stating that the lengths of the two tangent segments drawn from an external point to a circle are equal ($PA = PB$).

Hypotenuse-Side Test

A congruence criterion used for right-angled triangles stating that if the hypotenuse and one side of one right triangle are congruent to the hypotenuse and corresponding side of another right triangle, the two triangles are congruent ($\triangle OAP \cong \triangle OBP$).

c.s.c.t.

An abbreviation for 'corresponding sides of congruent triangles,' used to conclude that side lengths are equal once two triangles are proved congruent (e.g., $\text{seg } PA \cong \text{seg } PB$).

Componendo

An algebraic ratio and proportion operation where if $\frac{AX}{BX} = \frac{3}{2}$, then $\frac{AX + BX}{BX} = \frac{3 + 2}{2}$.

c.s.s.t.

An abbreviation for 'corresponding sides of similar triangles,' stating that corresponding sides of similar triangles are in proportion (e.g., $\frac{BA}{BX} = \frac{AC}{XY}$).

AA Similarity Test

A similarity criterion stating that if two angles of one triangle are congruent respectively to two corresponding angles of another triangle, the two triangles are similar ($\triangle BCA \sim \triangle BYX$).