7.4 Showing Triangles are
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1 7. howing riangles are imilar: and oal how that two triangles are similar using the and imilarity heorems. ey ords similar polygons p. he triangles in the avajo rug look similar. o show that they are similar, you can use the definition of similar polygons or the imilarity ostulate. In this lesson, you will learn two new methods to show that two triangles are similar. O 7.2 ide-ide-ide imilarity heorem () ords If the corresponding sides of two triangles are proportional, then the triangles are similar. ymbols If, then. 1 se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement and find the scale factor of riangle to riangle. olution ind the ratios of the corresponding sides. 1 2 Q Q 1 2 ll three ratios are equal. o, the corresponding sides of the triangles are proportional. y the imilarity heorem, Q. 1 he scale factor of riangle to riangle is howing riangles are imilar: and 7
2 tudent elp I hen using the imilarity heorem, compare the shortest sides, the longest sides, and then the remaining sides. Is either or similar to? 2 se the imilarity heorem olution 1 ook at the ratios of corresponding sides in and. hortest sides ongest sides emaining sides ecause all of the ratios are equal,. 2 ook at the ratios of corresponding sides in and. hortest sides ongest sides emaining sides ecause the ratios are not equal, and are not similar. se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement tudent elp OO o review included angles, see p. 22. O 7. ide-ngle-ide imilarity heorem () ords If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that include these angles are proportional, then the triangles are similar. ymbols If a c a and, then. 0 hapter 7 imilarity
3 se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement. 1 olution a and a both measure 1, so a ca. ompare the ratios of the side lengths that include a and a. horter sides onger sides 1 0 he lengths of the sides that include a and a are proportional. 1 y the imilarity heorem,. imilarity in Overlapping riangles how that. tudent elp I edraw overlapping triangles as two separate triangles, as shown on p.. olution eparate the triangles, and, and label the side lengths. a ca by the eflexive roperty of ongruence. horter sides onger sides he lengths of the sides that include a are proportional. y the imilarity heorem,. se the imilarity heorem etermine whether the triangles are similar. If they are similar, write a similarity statement. xplain your reasoning howing riangles are imilar: and 1
4 7. xercises uided ractice ocabulary heck kill heck 1. If two sides of a triangle are proportional to two sides of another triangle, can you conclude that the triangles are similar? In xercises 2 and, determine whether the triangles are similar. If they are similar, write a similarity statement Is either or similar to? xplain. 7 1 ractice and pplications xtra ractice ee p.. imilarity heorem etermine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of riangle to riangle omework lp xample 1: xs., 21 2 xample 2: xs xample : xs. 1 1, 21 2 xample : xs. 1,, hapter 7 imilarity
5 imilarity heorem Is either or similar to? xplain your reasoning rame uilding uppose you are constructing an -frame home that is modeled after a ski lodge. he ski lodge and home are shown below. re the triangles similar? xplain your reasoning. Itudent elp I O.O imilarity heorem etermine whether the two triangles are similar. If they are similar, write a similarity statement. OO xtra help with problem solving in xs. 1 is at classzone.com howing riangles are imilar: and
6 tudent elp I edraw overlapping triangles as two separate triangles, as shown on p.. Overlapping riangles how that the overlapping triangles are similar. hen write a similarity statement etermining imilarity etermine whether the triangles are similar. If they are similar, state the similarity and the postulate or theorem that justifies your answer ports huffleboard In the portion of a shuffleboard court shown,. 27. hat piece of information do you need in order to show that using the imilarity heorem? 2. hat piece of information do you need in order to show that using the imilarity heorem? O is played on a long flat court. layers earn points by using sticks called cues to push circular disks onto a scoring area at the opposite end of the court. ou be the udge 2. on claims that is similar to when x. ave believes that the triangles are similar when x. ho is right? xplain your reasoning. x 1 21 hapter 7 imilarity
7 tandardized est ractice echnology In xercises 0 and 1, use geometry software to complete the steps below. 1 raw. 2 onstruct a line perpendicular to &* through. abel the intersection. easure &*, &*, &*, and &*. alculate the ratios and. rag point until. 0. or what measure of a are and similar? 1. hat theorem supports your answer to xercise 0? 2. ultiple hoice hich method can be used to show that the two triangles at the right are similar? annot be shown. ultiple hoice In the diagram,. ind the value of x x 1 ixed eview sing isectors In the diagram below, &*( bisects a. (esson.). &* c _?_. a c _?_ 27. ma _?_ 7. Is a congruent to a? xplain your reasoning. olving roportions olve the proportion. (esson 7.1) b y 0. c a lgebra kills riting ecimals as ractions rite the decimal as a fraction in simplest form. (kills eview, p. 7) howing riangles are imilar: and
The hypotenuse and a leg of one triangle are congruent to the hypotenuse and a leg of the other triangle. THEOREM 5.2. right triangles, and
5.4 ypotenuse-eg ongruence heorem: oal se the ongruence heorem and summarize congruence postulates and theorems. ey Words hypotenuse p. 192 leg of a right triangle p. 192 he triangles that make up the
5.3 Proving Triangles are
0 1 1 10 5.3 roving riangles are ongruent: and Goal how triangles are congruent using and. ey Words vertical angles p. 75 alternate interior angles p. 121 Geo-ctivity 1 raw a segment 3 inches long. abel
Activity. Question. Materials. Explore. Think About It. Student Help. 1 On a piece of paper, draw a triangle and cut it out.
ctivity 4.6 Intersecting edians Question What is the relationship between segments formed by the intersection of the medians of a triangle? aterials straightedge scissors ruler xplore 1 On a piece of paper,
1.3 Points, Lines, and Planes
1.3 oints, ines, and lanes oal Use postulates and undefined terms. ey Words undefined term point, line, plane postulate collinear, coplanar segment ray he legs of the tripod touch the table at three points.
EXERCISES Practice and Problem Solving
XI ractice and roblem olving or more practice, see xtra ractice. ractice by xample xample (page 224) In each diagram, the red and blue triangles are congruent. Identify their common side or angle.. K 2.
Proof EXAMPLE EXAMPLE. Given:
4-7 hat ou ll earn o identify congruent overlapping triangles o prove two triangles congruent by first proving two other triangles congruent... nd hy o identify overlapping triangles in scaffolding, as
7.5 Proportions and. Similar Triangles. Geo-Activity. Goal Use the Triangle Proportionality Theorem and its converse.
7. roportions and imilar riangles Goal Use the riangle roportionalit heorem and its converse. Ke Words midsegment of a triangle Geo-ctivit 1 raw a triangle. Label its vertices,, and. Make sure that each
Altitudes and Perpendicular Bisectors
6 2 hat ou ll Learn ou ll learn to identify and construct s and perpendicular bisectors in triangles. ltitudes and erpendicular isectors In geometry, an of a triangle is a perpendicular segment with one
Objectives To use the AA Postulate and the SAS and SSS Theorems To use similarity to find indirect measurements
7-3 roving riangles imilar ontent tandards G..5 Use... similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.G.5 rove the slope criteria for parallel and
Using Corresponding Parts of Congruent Triangles
4-4 Using orresponding arts of ongruent riangles ontent tandards G..5 Use congruence... criteria for triangles to solve problems and prove relationships in geometric figures. lso G..12 bjective o use triangle
Work with a partner. Use dynamic geometry software. a. Construct ABC and DEF with the side lengths given in column 1 of the table below.
.3 roving riangle imilarity by and OMMO O Learning tandards HG-.. HG-..5 HG-G..5 HG-MG..1 OUIG VIL GUM o be proficient in math, you need to analyze situations by breaking them into cases and recognize
Proving Congruence ASA, AAS
roving ongruence, Vocabulary included side Use the ostulate to test for triangle congruence. Use the heorem to test for triangle congruence. are congruent triangles used in construction? he ank of hina
Isosceles Triangles. leg. base
6 4 What ou ll Learn ou ll learn to identif and use properties of isosceles triangles. Isosceles riangles ecall from Lesson 5 that an isosceles triangle has at least two congruent sides. he congruent sides
4-3. Triangle Congruence by ASA and AAS. Content Standard. Essential Understanding You can prove that two triangles are congruent
4-3 riangle ongruence by and ontent tandard G..5 Use congruence... criteria for triangles to solve problems and prove relationships in geometric figures. bjective o prove two triangles congruent using
Problem 2. Got It? Proving Triangle Parts Congruent to Measure Distance. Proof
4-4 Using orresponding arts of ongruent riangles ommon ore tate tandards G-..5 Use congruence... criteria for triangles to solve problems and prove relationships in geometric figures. lso G-..12 1, 3 bjective
11.5 Inscribed Angles and
age 1 of 6 11.5 Inscribed ngles and olygons Goal Use properties of inscribed angles. ey Words inscribed angle intercepted arc inscribed circumscribed n inscribed angle is an angle whose vertex is on a
EXERCISES Practice and Problem Solving
XI ractice and roblem olving For more practice, see xtra ractice. ractice by xample lgebra Find the value of x in each parallelogram. xample (page 95. 5.. 0. 56 5. 80 6. 6 xample (page 95 lgebra Find the
b. Move BC so that B is on the smaller circle and C is on the larger circle. Then draw ABC.
5.5 Proving Triangle ongruence by ssential uestion What can you conclude about two triangles when you know the corresponding sides are congruent? rawing Triangles Work with a partner. Use dynamic geometry
Angle Bisectors of Triangles
6 What You ll Learn You ll learn to identify and use angle bisectors in triangles. ngle isectors of Triangles ecall that the bisector of an angle is a ray that separates the angle into two congruent angles.
Essential Question How can you use congruent triangles to make an indirect measurement?
5.7 Using ongruent riangles ssential uestion How can you use congruent triangles to make an indirect measurement? easuring the Width of a iver IIUI H OI O OH o be proficient in math, you need to listen
To recognize congruent figures and their corresponding parts
4-1 ongruent igures ontent Standard Prepares for G.SR.5 Use congruence... criteria for triangles to solve problems and prove relationships in geometric figures. Objective o recognize congruent figures
6.3 Showing Quadrilaterals are
6.3 howing Quadrilaterals are arallelograms Goal how that a quadrilateral is a parallelogram. Key Words parallelogram p. 30 Geo-ctivity aking arallelograms ut two straws to form two congruent pairs. 2
Bisectors in Triangles
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Name Class Date. This shows that A corresponds to Q. Therefore, A Q. This shows that BC corresponds to RS. Therefore, BC RS.
Name lass ate eteaching ongruent igures iven, find corresponding parts using the names. rder matters. or example, or example, his shows that corresponds to. herefore,. his shows that corresponds to. herefore,.
Objectives To use relationships among sides and angles of parallelograms To use relationships among diagonals of parallelograms
6-2 roperties of arallelograms ontent tandards.o.11 rove theorems about parallelogram. s include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each
3. (9x + 9) x 45 5x. 5. (7x + 6)
5 hapter eview 5.1 ngles of riangles (pp. 231 238) ynamic Solutions available at igideasath.com lassify the triangle by its sides and by measuring its angles. he triangle does not have any congruent sides,
Essential Question How can you measure and classify an angle?
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1.6 Angles and Their Measures
1.6 ngles and heir Measures oal Measure and classify angles. dd angle measures. ey Words angle sides and vertex of an angle measure of an angle degree congruent angles acute, right, obtuse, and straight
Work with a partner. Use dynamic geometry software.
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Essential Question What are some properties of trapezoids and kites? Recall the types of quadrilaterals shown below.
7.5 Properties of Trapezoids and ites ssential Question What are some properties of trapezoids and kites? ecall the types of quadrilaterals shown below. Trapezoid Isosceles Trapezoid ite PV I OVI PO To
4-1. Standardized Test Prep. Multiple Choice. Short Response. Congruent Figures. For Exercises 1 6, choose the correct letter.
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Lesson 13.1 The Premises of Geometry
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Essential Question What are the properties of parallelograms?
7. roperties of arallelograms ssential uestion What are the properties of parallelograms? iscovering roperties of arallelograms Work with a partner. Use dynamic geometry software. a. onstruct any parallelogram
To identify congruence transformations To prove triangle congruence using isometries
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To identify congruence transformations To prove triangle congruence using isometries
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Key Concept Congruent Figures
4-1 ongruent igures ommon ore State Standards Prepares for G-SRT..5 Use congruence... criteria for triangles to solve problems and prove relationships in geometric figures. P 1, P 3, P 4, P 7 Objective
D AC BC AB BD m ACB m BCD. g. Look for a pattern of the measures in your table. Then write a conjecture that summarizes your observations.
OMMON O Learning tandard HG-O..0 6.6 Inequalities in Two Triangles ssential Question If two sides of one triangle are congruent to two sides of another triangle, what can you say about the third sides
Bisectors, Medians, and Altitudes
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4.2 pply ongruence and riangles oal p Identify congruent figures. Your Notes VOULRY ongruent figures orresponding parts o help you identify corresponding parts, turn n. xample 1 Identify congruent parts
To prove two triangles congruent using the SSS and SAS Postulates. Are the triangles below congruent? How do you know? 6 B 4
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Geometry 1A Homework 6.1b. Tell whether the ASA Postulate can be used to prove the triangles congruent. If not, write not possible
Geometry 1 omework 6.1b Name Name two triangles that are congruent by the ostulate. X W G I ell whether the ostulate can be used to prove the triangles congruent. If not, write not possible. 5. 30 0 30
8.1 Practice A. Name Date. Then find the area of XYZ. to the perimeter of XYZ.
ame ate.1 ractice In ercises 1 and 2, find the scale factor. hen list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. 1. 2. GH 13
Proving Congruence SSS, SAS
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Segments, Rays, Parallel Lines and Planes Q L R M. Segment AB. Endpoint. Ray YX. Naming Segments and Rays
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Identify similar figures. Solve problems involving scale factors. do artists use geometric patterns?
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5 Congruent Triangles
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7.3 Similar Right Triangles
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2.7 Angles and Intersecting Lines
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Chapter 4 Answers. Practice m 1 = 110; m 2 = m 3 = 90; m 4 = m 5 = 140; m 6 = 90; m 7 = 40; m 8 = 90
Pearson ducation, Inc., publishing as Pearson Prentice all. ll rights reserved. hapter 4 nswers Practice 4-1 1. m 1 = 110; m 2 = 120 2. m 3 = 90; m 4 = 135 3. m 5 = 140; m 6 = 90; m 7 = 40; m 8 = 90 4.
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