Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks to arrange the steps for constructing triangle $XYZ$ given that $XY = 10$ cm, $XZ =...
Triangle ConstructionEuclidean GeometryGeometric Construction
2025/6/16
Given three vectors $\vec{a} = 6\hat{i} + 3\hat{j} - 9\hat{k}$, $\vec{b} = 12\hat{i} - 8\hat{j} - 4\...
VectorsDot ProductCross ProductScalar Triple ProductVector Triple Product3D Geometry
2025/6/15
The problem asks to prove the Angle Sum Theorem for a triangle, which states that the sum of the int...
Angle Sum TheoremTrianglesGeometric ProofParallel LinesAlternate Interior Angles
2025/6/15
We are given a triangle $ABC$ with an angle $A = 55^\circ$. We are also given that $DE$ is parallel ...
TrianglesParallel LinesAnglesGeometric Proof
2025/6/15
The problem describes a geometric construction. It asks us to: i. Construct triangle ABC with $AB = ...
Geometric ConstructionTrianglesTrapeziumsCirclesArea CalculationAnglesParallel LinesPerpendicular Bisector
2025/6/15
The problem asks to perform a series of geometric constructions and calculations based on the given ...
Geometric ConstructionTrianglesTrapeziumsCirclesAnglesArea CalculationLaw of Cosines
2025/6/15
Given that vectors $\vec{a}$, $\vec{b}$, and $\vec{c}$ are coplanar, we need to show that the determ...
VectorsDeterminantsLinear AlgebraCoplanar VectorsDot Product
2025/6/15
We need to show that the four points $A = -6i + 3j + 2k$, $B = 3i - 2j + 4k$, $C = 5i + 7j + 3k$, an...
Vectors3D GeometryCoplanar PointsScalar Triple ProductDeterminants
2025/6/15
We need to prove that the scalar triple product of the vectors $a+b$, $b+c$, and $c+a$ is equal to t...
Vector AlgebraScalar Triple ProductVector Operations3D Geometry
2025/6/15
The problem asks us to find the volume of a tetrahedron with vertices $A(2, -1, -3)$, $B(4, 1, 3)$, ...
3D GeometryVolumeTetrahedronVectorsScalar Triple ProductCross Product
2025/6/15