Triangle + the proof - practice problems
Number of problems found: 15
- Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - Bisector 2
ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC. - Triangle
Prove whether you can construct a triangle ABC if a=8 cm, b=6 cm, c=10 cm. - Proof PT
Can you easily prove Pythagoras' theorem using Euclidean theorems? If so, do it.
- Inequality 4434
The heel of height from the vertex C in the triangle ABC divides the side AB in the ratio 1:2. Prove that in the usual notation of the lengths of the sides of the triangle ABC, the inequality 3 | a-b | holds - Isosceles 83157
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Triangle P2
Can a triangle have two right angles? - Triangle 80994
In the triangle, ABC, the angles alpha and beta axes subtend the angle phi = R + gamma/2. R is a right angle of 90°. Verify. - Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri
- Diagonal in rectangle
In the ABCD rectangle is the center of BC, point E, and point F is the center of the CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Trapezoid 4908
Trapezoid ABCD with bases AB = a, CD = c has height v. The point S is the center of the arm BC. Prove that the area of the ASD triangle is equal to half the area of the ABCD trapezoid. - Constructed 77874
Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their contents are the same. - Intersection 7247
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Prove
Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
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