In Triangles | Unit 5 Test Study Guide Relationships

Here’s a for a typical Unit 5: Relationships in Triangles (commonly from Geometry courses like Pearson, Eureka, or Texas TEKS).

In ( \triangle ABC ), ( AB=5, BC=7, AC=9 ). Which angle is largest? Largest side ( AC ) → opposite ( \angle B ) is largest. 7. Hinge Theorem (SAS Inequality) If two sides of one triangle are congruent to two sides of another, and the included angle of the first is larger, then the third side of the first is longer.

Triangles ( ABC ) and ( DEF ) have ( AB=DE, AC=DF ), ( \angle A=80^\circ, \angle D=60^\circ ). Compare ( BC ) and ( EF ). ( BC > EF ) 8. Exterior Angle Theorem Exterior angle = sum of two remote interior angles. unit 5 test study guide relationships in triangles

In ( \triangle ABC ), median ( AD ) has ( AG = 8 ). Find ( GD ). ( \fracAGGD = \frac21 ) → ( 8/GD = 2 ) → ( GD = 4 ) 5. Altitudes & Orthocenter Altitude: Perpendicular segment from vertex to opposite side (or extension).

Can sides 4, 7, 12 form a triangle? ( 4+7 = 11 \not> 12 ) → No. Angle-Side Relationship: Largest angle opposite largest side, smallest angle opposite smallest side. Here’s a for a typical Unit 5: Relationships

Triangle ( ABC ) has midpoints ( D ) on ( AB ) and ( E ) on ( AC ). If ( BC = 18 ), find ( DE ). Answer: ( DE = 9 ) 2. Perpendicular Bisectors & Circumcenter Perpendicular bisector: A line/segment/ray perpendicular to a segment at its midpoint.

I’ll organize it by , theorems , formulas , and example problem types you’ll likely see on the test. 1. Midsegments of a Triangle Definition: A segment connecting the midpoints of two sides of a triangle. Largest side ( AC ) → opposite ( \angle B ) is largest

If third sides differ, the angle opposite the longer side is larger.