Presentation on theme: "Applying Properties 7-4 of Similar Triangles Warm Up"— Presentation transcript:




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1 Applying Properties 7-4 of Comparable Triangles Warm UpLesboy Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

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2 Warm Up Solve each propercent. AB = 16 QR = 10.5 x = 21 y = 8

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3 Objectives Use properties of comparable triangles to find segment lengths. Apply proportionality and also triangle angle bisector theorems.

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4 Artists usage mathematical techniques to make two-dimensional paints show up three-dimensional. The innovation of perspective was based on the observation that far amethod objects look smaller and closer objects look larger. Mathematical theorems favor the Triangle Proportionality Theorem are necessary in making perspective illustrations.

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6 Example 1: Finding the Length of a SegmentFind US. It is offered that , so by the Triangle Proportionality Theorem. Substitute 14 for RU, 4 for VT, and 10 for RV. US(10) = 56 Cross Products Prop. Divide both sides by 10.

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7 Check It Out! Example 1 Find PN. Use the Triangle Proportionality Theorem. Substitute in the offered worths. Cross Products Prop. 2PN = 15 PN = 7.5 Divide both sides by 2.

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9 Example 2: Verifying Segments are ParallelVerify that Because , by the Converse of the Triangle Proportionality Theorem.

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10 Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that Due to the fact that , by the Converse of the Triangle Proportionality Theorem.

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12 Example 3: Art ApplicationSuppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and also KL = 4.9 in., uncover LM and MN to the nearest tenth of an inch.

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13 Example 3 Continued Given 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 2.6 for BC. 4.5(LM) = 4.9(2.6) Cross Products Prop. LM  2.8 in. Divide both sides by 4.5.

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14 Example 3 Continued 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD. 4.5(MN) = 4.9(4.1) Cross Products Prop. MN  4.5 in. Divide both sides by 4.5.

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15 Check It Out! Example 3 Use the diagram to discover LM and also MN to the nearest tenth.

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16 Check It Out! Example 3 ContinuedGiven 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and also 1.4 for BC. 2.4(LM) = 1.4(2.6) Cross Products Prop. LM  1.5 cm Divide both sides by 2.4.

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17 Check It Out! Example 3 Continued2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 2.2 for CD. 2.4(MN) = 2.2(2.6) Cross Products Prop. MN  2.4 cm Divide both sides by 2.4.

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18 The previous theorems and corollary bring about the following conclusion.

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19 Example 4: Using the Triangle Angle Bisector TheoremFind PS and also SR. by the ∆  Bisector Theorem. Substitute the provided values. 40(x – 2) = 32(x + 5) Cross Products Property 40x – 80 = 32x + 160 Distributive Property

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20 Example 4 Continued 40x – 80 = 32x + 160 8x = 240 Simplify. x = 30 Divide both sides by 8. Substitute 30 for x. PS = x – 2 SR = x + 5 = 30 – 2 = 28 = = 35

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21 Check It Out! Example 4 Find AC and also DC. by the ∆  Bisector Theorem. Substitute in offered worths. 4y = 4.5y – 9 Cross Products Theorem –0.5y = –9 Simplify. y = 18 Divide both sides by –0.5. So DC = 9 and also AC = 16.

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22 Leschild Quiz: Part I Find the size of each segment. SR = 25, ST = 15

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23 Leskid Quiz: Part II 3. Verify that BE and also CD are parallel.

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Since , by the Converse of the ∆ Proportionality Thm.

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