Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

We are given a figure with two parallel lines $p$ and $q$, intersected by transversals $j, k, m, n$....

Parallel LinesAnglesTransversalsCorresponding AnglesSupplementary Angles
2025/4/1

We are given a diagram with lines $j$, $k$, $m$, $n$, $p$, and $q$. We know that $m\angle 1 = 50^\ci...

AnglesParallel LinesTransversalsSupplementary AnglesVertical AnglesCorresponding Angles
2025/4/1

Given that $m\angle 9 = 75^{\circ}$, find the measure of the following angles: $\angle 3$, $\angle 5...

AnglesParallel LinesTransversalsCorresponding AnglesVertical AnglesSupplementary Angles
2025/4/1

The image shows a right triangle $\triangle LMN$ with a right angle at $L$. Point $P$ is on $NM$ suc...

Similar TrianglesRight TrianglesGeometric MeanProportions
2025/4/1

We are given a triangle $PQR$ with a line segment $YX$ parallel to $QR$. The length of $PY$ is 2, th...

Similar TrianglesProportionsParallel LinesTriangle Properties
2025/4/1

We are given a right triangle FGH, where angle G is a right angle. The length of the side FH is 98, ...

TrigonometryRight TrianglesSineAnglesArctangent
2025/4/1

We are given a right triangle $KLM$ with a right angle at $L$. We are given that side $LM$ has lengt...

TrigonometryRight TrianglesCosineTriangle GeometryAngle Measurement
2025/4/1

We are given a triangle $LMN$ with a right angle at $L$. $LP$ is perpendicular to $NM$. We are given...

Similar TrianglesRight TrianglesProportionsPythagorean Theorem (implicitly used)
2025/4/1

The problem asks to solve for $x$ in the right triangle $LMN$. We are given that angle $N$ is $64^\c...

TrigonometryRight TrianglesTangentAngle of ElevationTriangle Properties
2025/4/1

The problem provides a right triangle $\triangle LMN$ with $\angle L = 90^\circ$. A perpendicular l...

TrianglesRight TrianglesSimilar TrianglesPythagorean Theorem
2025/4/1