📐 geometry

1. Énoncé du problème : Montrer que $\overrightarrow{CA} = \frac{1}{2} \overrightarrow{AB} + \frac{1}{3} \overrightarrow{AE}$ et en déduire que $C$ est le milieu de $[AC]$.

1. **Énoncé du problème** : Considérons le parallélogramme ABCD avec les points E et G définis par :

1. Énoncé : Dans le parallélogramme ABCD, les points E et H sont définis par : $AE=\frac{3}{2}AB$ et $CH=\frac{1}{2}CA+\frac{3}{2}CB+2AE=0$. 2. Montrer que $AH=\frac{1}{2}AB+\frac{

1. **Problem 1:** Given: circle X is congruent to circle B, and line XZ = line BD. 2. We want to prove line WY is congruent to line AC.

1. **Problem statement:** We have a square lot with a true area of 2.25 hectares. The sides were measured using a tape that is 0.04 m too short (each measurement is underestimated

1. Stel die probleem: Gegee is 'n gelyksydige driehoek ABC met sy lengtes van 20 cm. Binnenin hierdie driehoek is 'n reghoek DEFG met punte D en G op die sye AB en AC onderskeideli

1. **State the problem:** We need to find the area swept by the policeman's arm, which moves through an angle of 75° with a length (radius) of 60 cm. 2. **Understand the geometry:*

1. The problem asks for a point P on the y-axis equidistant from points A(-5, 5) and B(3, 7). 2. Since P lies on the y-axis, its x-coordinate is 0, so P = (0, y).

1. **State the problem:** We have an equilateral triangle with vertices\nA(0, -2), B(0, -10), and C(4\sqrt{3}, y), where $y < 0$. We need to find the value of $y$.\n\n2. **Calculat

1. We are given a triangle ABC with a right angle at H, where H is the projection of A on BC, and AH is perpendicular to BC. 2. Given lengths: AB = 6, BH = 4, HC = 5.

1. Problem (6): In triangle $\triangle ABC$, given $AC > AB$, point $M$ lies on $AC$, and $m(\angle ABM) = m(\angle C)$. Prove that $AB^2 = AM \times AC$. 2. Since $m(\angle ABM) =

1. **Identify and name given parts of the circle** - 1. $RT$: From the problem context, this corresponds to a radius (segment from center to point on circle) so answer is D. Radius

1. **Problem Statement:** Point P lies on side CD of cyclic quadrilateral ABCD such that \(\angle CBP = 90^\circ\). Let K be the intersection of AC and BP such that \(AK = AP = AD\

1. The problem asks to find the diagonal of a square with side length 5 cm. 2. Recall that the diagonal $d$ of a square with side length $s$ is given by the formula:

1. **State the problem:** We want to find the measure of angle $\angle QTN$ given two expressions related to angles involving $x$: $(2x + 55)^\circ$ and $(7x + 25)^\circ$. 2. **Ana

1. The problem asks to find the diagonal of a rectangle with width 2 feet and length 4 feet. 2. Recall that the diagonal $d$ of a rectangle can be found using the Pythagorean theor

1. **State the problem:** We need to find the measure of angle $\angle GKL$ given the expressions for angles at points $K$ and $L$ as $(8x + 11)^\circ$ and $(7x - 41)^\circ$.\n\n2.

**Problem C: Solve for $x$ in each of the given chord segments using the chord segment theorem.** 1. Given segments: $2$, $x$, $12$, $8$.

1. The problem gives two parallel lines IJ and KL crossed by a transversal GH, with angles at points M and N: (7x - 65)° and 56° respectively. 2. Since IJ and KL are parallel, angl

1. **Problem statement:** We have a 3D figure made of five cubes in an L-shape, with one cube stacked above the leftmost cube in the vertical part.

1. The problem asks to draw the shape of a right angle triangle. 2. A right angle triangle is a triangle that has one angle equal to $90^\circ$.