<p>Write one statement per line, followed by its reason. Mark given facts first and use only these or earlier deductions.</p>
<p>Example: \(\angle ABD=90^\circ\) (angle in a semicircle).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 560px;"><colgroup><col style="width: 42.8571%;"><col style="width: 57.1429%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Situation</strong></th><th style="text-align: center; --cell-justify: center"><strong>Reason to quote</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Angles at a point, on a straight line, vertically opposite</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Parallel lines \(AB//CD\)</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Triangle angle facts</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Congruent triangles</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Similar triangles</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Chords of a circle</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Tangents</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Angles in a circle</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Tangent and chord; midpoints of sides</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p>Name corresponding triangle vertices in the same order. Finish with the result required.</p>

Write one statement per line, followed by its reason. Mark given facts first and use only these or earlier deductions.

Example: \(\angle ABD=90^\circ\) (angle in a semicircle).

Angles at a point, on a straight line, vertically opposite

(\(\angle\)s at a point)
(adj. \(\angle\)s on a str. line)
(vert. opp. \(\angle\)s)

(corr. \(\angle\)s, \(AB//CD\))
(alt. \(\angle\)s, \(AB//CD\))
(int. \(\angle\)s, \(AB//CD\))

(\(\angle\) sum of \(\triangle\))
(ext. \(\angle\) of \(\triangle\))
(base \(\angle\)s of isos. \(\triangle\))

(AA similarity), (SSS similarity), (SAS similarity)

(\(\perp\) bisector of chord)
(equal chords, equidistant from centre)

(tangent \(\perp\) radius)
(tangents from an external point)

(\(\angle\) in semicircle)
(\(\angle\) at centre \(=2\angle\) at circumference)
(\(\angle\)s in the same segment)
(\(\angle\)s in opposite segments)

(Alternate Segment Theorem)
(Midpoint Theorem)

Name corresponding triangle vertices in the same order. Finish with the result required.

Writing a Geometric Proof

Writing a Geometric Proof

Situation	Reason to quote
Angles at a point, on a straight line, vertically opposite
Parallel lines \(AB//CD\)
Triangle angle facts
Congruent triangles
Similar triangles
Chords of a circle
Tangents
Angles in a circle
Tangent and chord; midpoints of sides