Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
Given a square $ABCD$, where $CE$ is parallel to $BD$, and $E$ belongs to $AD$. a) Prove that $\vec{...
VectorsGeometrySquaresVector AdditionVector Proofs
2025/3/29
Given a regular hexagon $ABCDEF$, let $A_1, B_1, C_1, D_1, E_1, F_1$ be the midpoints of the sides $...
VectorsGeometryHexagonMidpointVector Addition
2025/3/29
Given a parallelogram constructed on vectors $\vec{AB}$ and $\vec{AD}$, express the vectors $\vec{OA...
VectorsParallelogramVector AdditionMidpoint
2025/3/29
Given a regular hexagon $ABCDEF$, with $\vec{AB} = \vec{p}$ and $\vec{BC} = \vec{q}$, express the ve...
VectorsGeometryHexagon
2025/3/29
Given a triangle $ABC$ with $\vec{AC} = \vec{a}$ and $\vec{BC} = \vec{b}$. A square $ACDE$ is constr...
VectorsGeometrySquaresVector Addition2D Geometry
2025/3/29
Given that $\vec{a} \times \vec{b} = \vec{c} \times \vec{d}$ and $\vec{a} \times \vec{c} = \vec{b} \...
Vector AlgebraCross ProductVector EquationsParallel Vectors
2025/3/29
We are given a graph of a line and are asked to find the following: (a) The y-intercept of the line....
Linear EquationsSlopeY-interceptStandard Form of a LineCoordinate GeometryGraphing
2025/3/28
The problem asks us to find the three inequalities that define the unshaded region R in the given gr...
Linear InequalitiesCoordinate GeometryGraphing
2025/3/28
The problem asks us to find the measure of the major arc MDN of a circle, given that the central ang...
CircleArcCentral AngleMajor ArcAngle Measurement
2025/3/28
We are given a circle with center $O$. The measure of the central angle $\angle MON$ is $67^\circ$. ...
CircleArcCentral AngleMajor Arc
2025/3/28