Given: QR I PT and ZQPR = ZSTR Angles Segments Triangles Statements Reasons
Prove: APQR - ATSR
ZQPR
ZQRP
ZSRT
ZSTR
Q
Statements
Reasons
S
R
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Intro

To prove that Triangles PQR and TSR are similar triangles, the following are the complete two-column proof stating the statements with their reasons:

S1: QR is perpendicular to PT

R1: Given

S2: <QRP and <SRT are right angles

R2: Definition of perpendicular

S3: <QPR = <STR

R3: Given

S4: <QRP = <SRT

R4: All right angles are congruent

S5: Triangle PQR is similar to triangle TSR

R5: AA Similarity Theorem

Therefore, to prove that Triangles PQR and TSR are similar triangles, the following are the complete two-column proof statimg the statements with their reasons:

S1: QR is perpendicular to PT

R1: Given

S2: <QRP and <SRT are right angles

R2: Definition of perpendicular

S3: <QPR = <STR

R3: Given

S4: <QRP = <SRT

R4: All right angles are congruent

S5: Triangle PQR is similar to triangle TSR

R5: AA Similarity Theorem

Learn more about AA Similarity Theorem on:

link

Step-by-step explanation:

Given :

QR⊥PT

To Prove :

Solution:

Statements                                            Reasons

QR⊥PT                                                Given

∠QRP and ∠SRT are right angles       Def of perpendicular

∠QPR≅∠STR                                     Given

∠QRP = ∠SRT                                    All right angles are equal

ΔPQR≈ΔTSR                                     AA similarity

Hence  

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.