mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Equal side and angle

In the diagram shown, the lengths \(AD = CD\) and the angles \(ABD=CBD\).
Prove that the lengths \(AB=BC\).

Show answer

If you enjoyed this puzzle, check out Sunday Afternoon Maths XXXVIII,
puzzles about triangles, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

expansions indices differentiation polygons square numbers binary area pascal's triangle quadratics square grids algebra polynomials colouring lines regular shapes parabolas 2d shapes tiling circles coins perfect numbers numbers menace number tangents dates sport dodecagons products speed rectangles the only crossnumber determinants functions time advent symmetry 3d shapes grids consecutive numbers cryptic crossnumbers cube numbers prime factors multiplication shapes games wordplay triangles palindromes dice sum to infinity clocks sets spheres quadrilaterals partitions prime numbers proportion lists cards crosswords books planes complex numbers elections scales coordinates ellipses multiplaction squares integers angles sequences dominos chess division digital clocks axes taxicab geometry decahedra square roots integration geometric means people maths cryptic clues rugby sums factors arrows probabilty geometry money combinatorics addition irreducible numbers odd numbers chalkdust crossnumber even numbers digits triangle numbers graphs folding tube maps volume christmas doubling range surds remainders consecutive integers averages medians floors unit fractions tournaments trigonometry star numbers balancing shape means perimeter gerrymandering logic median matrices percentages mean powers factorials albgebra fractions squares bases ave probability crossnumbers xor cubics pentagons hexagons chocolate digital products neighbours routes multiples geometric mean calculus

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026