## Geometry Formulas

No matter how many types of questions you will see, the use of Geometry formulas and rules has a lot of impact and contribution to the final answer.

In the TYT-AYT Mathematics test; It becomes important to reach shorter, practical, solution-oriented results.Most of the time, you can reach the result of the problem by combining several different formulas.Most importantly, you know when and how to apply it.Ders Geometri guides you through the most important formulas.

### Why Are Geometry Formulas Important?

Solving geometry questions; A certain level of knowledge, whose logic is grasped, requires a highly attentive and experienced perspective. In this, geometry formulas are used. Mathematical expressions that require many operations are poured into formulas, making it possible to answer questions quickly and practically.

Since the subjects are related to each other, the solution ways of the problem are seen more easily as a result of using formulas with different and different methods. In addition, the possibility of falling into operation errors is reduced.

However, the building blocks of the Geometry lesson, which are frequently encountered in problems, are to know the formulas of tales, basic similarity, euclid, and cosine, especially the Pythagorean relation; allows practice.

### How Do We Keep Geometry Formulas in Mind?

The more you practice and use equations and formulas, the more you will remember the application of formulas. The best way to keep formulas in mind is by reviewing and practicing them daily.

You should gain experience by practicing a lot, progressing step by step. The experience you have gained will inevitably lead you to use mathematical-geometry formulas. In this way, you will have the formulas memorable, that is, you will both understand and memorize them.

Then, you will be able to reach the result of the problem more easily, and you will be able to prove theorems.

As you proceed to the next level, you will notice that the same basic concepts of geometry, axioms and theorems are used as the point inside the point that repeats continuously.

You can examine the images and download the PDF file from the end of the page to your computer.

Geometry Shalwar-Boomerang-Missile-Rocket Rule

In a concave-concave quadrilateral as in the figure, (the measure of the angle formed when the triangle’s edge is bent in) it is formulated with x = a + b + c.

Two Internal Angle Diagram Angle Formula

The angle formed by two inner bisectors in a triangle is 90 ° more than half the size of the inner angle in the third corner.

Two Outside Angle Diagrams Formula

The measure of the angle formed by the two outer bisectors in a triangle is all half the measure of the angle in the third corner. In other words, the angle formed by the two outer bisectors in a triangle is less than 90 ° by half the angle in the third corner.

Inner and Outer bisector Angle Formula

The measure of the angle formed by the bisectors of a non-adjacent interior angle and an exterior angle in a triangle is equal to half the measure of the angle in the third corner.

Triangle Inequality Formula

One side length in a triangle; is less than the sum of the lengths of the other two sides and greater than the absolute value of the difference.

If the side lengths of triangle ABC in the figure are a, b, c; |b-c|<a<b+c, |a-c|<b<a+c, |a-b|<c<a+b.

Triangle Inequality Environment Formula

The sum of the lengths of any point taken in a triangle ABC to the vertices of the triangle; half of the triangle is larger than its circumference and smaller than its circumference.

In the triangle ABC in the figure, where | BC | = a, | AC | = b, | AB | = c and a + b + c = 2u; u <| KA | + | KB | + | KC <2u.

Tales Theorem Formula

On any two lines that intersect parallel lines, the line segments separated by parallels are proportional.

In the figure d1 // d2 // d3, if m and n lines intersect; | AB | / | BC | = | DE | / | EF |, | AB | / | AC | = | DE | / | DF | and | BC | / | AC | = | EF | / | DF |.

Fabulous Triple Formula

In a right triangle, the median of the hypotenuse is equal to half the length of the hypotenuse. In other words, in a right triangle the midpoint of the hypotenuse is equidistant from the vertices.

In triangle ABC in the figure, m (A) = 90 ° and | BD | = | DC | if; | BD | = | DC | = | AD |.

Special Angled Triangle Formulas

If the length of the side opposite a 30 ° angle in a right triangle is x units; the length of the hypotenuse is 2x units, and the length of the side opposite the angle of 60 ° is x root3 units.

In a 15 ° -75 ° -90 ° right triangle, the height of the hypotenuse is one quarter of the hypotenuse.

Special Triangle Formulas

In an isosceles triangle, the sum of the posts lowered to equal sides from a point taken on the base is equal to a height belonging to the equal sides.

In the figure; If | AB | = | AC |, [DF] ⊥ [AC], [DE] ⊥ [AB]; | BN | = | ED | + | DF |.

Special Triangle Formulas

In an isosceles triangle, the sum of the lengths of the parallel line segments drawn from a point on the base to equal sides is equal to the length of one of the equilateral sides.

Special Triangle Formulas

The absolute value of the difference in lengths of the perpendiculars descending to the equal sides of the triangle from a point taken on the extension of the base of the isosceles triangle is equal to a height belonging to the equal sides.

In the figure; If | AB | = | AC |, [EP] ⊥ [AC], [EF] ⊥ [AF] and [BN] ⊥ [AC]; | EP | – | EF | = | BN |.

Special Triangle Formulas

The square of the length of the line segment drawn from the vertex to the base in an isosceles triangle is equal to the difference of the length of the sides divided by the square of the length of one of the equilateral sides.

In the triangle ABC in the figure, with | AB | = | AC | = b, | AD | = x, | BD | = m and | DC | = n; x² = b²-m.n.

Special Triangle Formulas

In the figure, if ABC is an equilateral triangle, [DE] ⊥ [AE], [DT] ⊥ [BC], [DF] ⊥ [AF] | AB | root3 / 2 = | ED | + | DF | – | DT |.

Inner Angle bisector Theorem formula

In a triangle, the bisector length divides the opposite side in proportion to its neighboring sides.

If the triangle ABC in the figure [AN] is the bisector; | AB | / | BN | = | AC | / | CN |.

Outer Angle bisector Theorem formula

In triangle ABC in the figure [AD]; The bisector of m (CAE), with | CD | = x, | BC | = a, | AC | = b and | AB | = c; x / (x + a) = b / c

Outer bisector length formula

In the triangle ABC in the figure, [AN] inner bisector, [AD] outer bisector, | CD | = x, | NC | = n and | BN | = m; x / (x + n + m) = n / m.

Outer bisector length formula

In the triangle ABC in the figure, [AD] outer bisector, | CD | = x, | BC | = a, | AC | = b, | AB | = c and | AD | = y; y² = x. (x + a) -bc.

Area Relation in Geometry Triangle

The height of the hypotenuse in a right triangle is the product of the lengths of the perpendicular sides divided by the length of the hypotenuse.

In the triangle ABC in the figure, [BA] ⊥ [AC], [AD] ⊥ [BC], | AB | = c br, | AC | = b br, | BC | = a br and | AD | = h br; h = (c.b) / a is the unit.

Triangle Area Rules

In any triangle ABC, the median length of an edge divides the area of ​​the triangle into two equal areas.

In the triangle ABC in the figure, | BF | = | FC | if; Area (ABF) = Area (AFC).

Internal Angle Diagram Rules

If a triangle has two inner bisectors, the third is the inner bisector. In a triangle, the inner bisectors intersect at a point inside the triangle. This point is the center of the triangle’s inner tangent circle.

If [BP], [CP] in triangle ABC in the figure; [AP] is bisector.

Median Theorem Formula

In the triangle ABC in the figure, if BC | = a br, | AC | = b br, | AB | = c br, | AP | = Va br, | BR | = VB br, | CS | = VC br; 2Va² = b² + c²-a² / 2, 2Vb² = a² + c²-b² / 2 and 2Vc² = a² + b²-c² / 2.

Medium and U Area Formula

A triangle ABC with side lengths a, b, c and median lengths Va, Vb, Vc; 4 (Va² + Vb² + Vc²) = 3 (a² + b² + c²).

If the radius r of the inner tangent circle of a triangle, the sides are a, b, c and u = (a + b + c) / 2; Area (ABC) = u.r.

Sinusoidal Area Formula in Triangle

If m (ADB) = α in triangle ABC in the figure; The area of ​​the concave quadrilateral is A (ABEC) = (1/2). | AE |. | BC | .sinα.

In any quadrilateral; diagonals | CA | = e, | DB | = f with angle between α; Area (ABCD) = (1/2) .e.f.sinα..

In a rectangle whose diagonals intersect perpendicularly, the sum of squares of opposite sides is equal to each other. (A² + c² = b² + d²)

Steep Trapezoid Formula

In a vertical trapezoid, if the diagonals are perpendicular to each other, the height is the geometrical middle of the lower and upper base. (Height squared equals the product of the bases.)

The quadrilateral ABCD in the figure is [CD] ⊥ [DA], [DA] ⊥ [CD], [DB] ⊥ [AC], | AB | = a br, | CD | = c br and | DA | = h br; h = √ac.

Area Rules on Trapezoid

The midpoint of one of the side edges in a trapezoid; The area of ​​the triangle obtained when joined by two opposite vertices is equal to half the area of ​​the trapezoid.

ABCD trapezoid and | CA | = | DB | if; A (DAE) = (1/2) .A (ABCD).

If the midpoints of the sides of a quadrilateral are connected, a parallelogram is formed.

The midpoints of the N, P, K, L sides in the quadrant ABCD in the figure; A (NPKL) = (1/2). A (ABCD).

Field Rules in Parallelograms

The sum of the areas of the two triangles obtained when any point taken outside the parallelogram is joined to the vertices of the parallelogram is equal to half the area of ​​the parallelogram

In the figure ABCD is a parallelogram and a point P taken outside; A (PDA) + A (PBC) = (1/2). A (ABCD).

### TYT-AYT Geometry Formulas and Proofs PDF

Course Geometry offers important Geometry formulas in pdf format that can be downloaded free of charge. Students can view the Geometry Mathematics formulas pdf, which is important for TYT-AYT, which aims to improve students' problem solving skills. Candidates should apply these formulas to the questions.