Figures that have the same size and shape

Figures that have the same size and shape ∆ABC ≅ ∆DEF You couldn't say ∆ABC ≅ ∆FDE because the corresponding parts don't match. The order corresponding figures are named matters since the corresponding parts MUST line up in the name. Sides or angles that are in the same place in congruent figures

Objects are often drawn in different orientations to test your ability to correctly identify corresponding parts. FGH ∠G ∠F FG GH m∠W 60 12 HF WX y-x y - 12 5 x + 5 5 x 18 ∠H

∠F ∠G ∠H ∠J ≅ ≅ ∠S ∠T ∠U ∠V FG ≅ ST GH ≅ TU HJ ≅ UV JF ≅ VS m∠G = m∠T 2 x - 7 = 103 2 x = 110 x = 55 m∠G = 2 x - 7 m∠G = 2(55) -7 m∠G = 103

∠ Q This is a paragraph proof ∠ 3 ∠ RS 4 Alternate Int ∠'s Theorem congruent RS Reflexive Property congruent SP ∆RSP size Yes shape

congruent Vertical Angles Theorem ∠VWU ∠ V 180° - 66° - 44° 70°

Remember, the Reflexive Property is used when a side or angle is shared between shapes. HG ≅ HG ∠F ≅ ∠J Given HG ≅ HG Given ∠F ≅ ∠J Definition of ≅ ∆'s

∆ABC ∆DEF ≅ ∆ABC ≅ ∆JKL

From the diagram, AB ≅ CD. Point E is the midpoint of AC and BD. Therefore, AE ≅ CE and BE ≅ DE by the definition of midpoint. This means all the corresponding sides are congruent. The diagram shows AB ∥ CD, so ∠A ≅ ∠C by the Alt. Int. ∠'s Thm. Also, ∠AEB ≅ ∠CED by the Vertical ∠'s Thm. All corresponding parts are congruent, so ∆ABE ≅ ∆CDE. m∠D = 180 - 71 - 47 =62 You must also know that AB ≅ DE and BE ≅ CE to conclude that ∆ABE ≅ ∆DCE.